text:
Hello World 0.0!

 source: Dilbert, September 8, 1992

I'm hoping to add a new twist on the classic "Hello World!" program.
Code a program that outputs Hello World! without:

String/Character literals
Numbers (any base)
Pre-built functions that return "Hello World!"
RegEx literals

With the exceptions of "O"† and 0.
†"O" is capitalized, "o" is not acceptable.

I hope by "numbers" you mean "numeric constants", because there probably wouldn't be much programming left without.

Numeric literals/constants, yes.

So stuff like ?! (character value of "!" in Ruby 1.8) would be allowed, then?

I'm not familiar with Ruby's syntax, is ?! a special string literal? I consider RegEx literals like /Hello World/ to be too similar to string literals.

In Ruby 1.8, ?x is the character value of the character x. So for example ?a is 97, ?A is 65 and ?! is 33. It's not a string, I'm just not sure if it fits your definition of a numeric literal.

One of [code-golf] and [code-challenge] please, not both. The point of these tags to to help people find questions with the rules they want to use. Essentially every question on this site should be a game of some kind or another.

-1 We've already had Obfuscated Hello World, and I think this challenge is too similar. I'd have cast a "close as duplicate" vote, if I weren't a mod.

@Chris Jester-Young, I feel that this version of the hello world problem is different enough, if purely because it's more difficult. It'd be like saying this should be closed just because it's a "Hello World" problem.

@zzzzBov: I don't think it's different enough to warrant another question in the "hello world" theme; a different theme would have been better. But, that's just my opinion.

I think this is a fine code golf - and better than the prior one.

Some people seem to assume that "O"* means they can have a string literal with any number of O’s, including zero. I don’t think that was the intention. Please clarify.

@Timwi, Multiple "O"s are fine, "" (an empty string literal) is not. Dilbert never mentioned using single "O"s in his programs.

BTW, where did that comic come from?

@KevinCox, I completely forgot to credit the source! It's a Dilbert comic from 1992.

I thought it looked like Dilbert, it's amazing how the art style has changed though.

Can I even use Bash, given that command-line arguments are literals AFAIK?

How would you solve this in Seed?

Are we allowed to output Hello, World with a comma?

@VFDan, no the question clearly shows the output as it is expected.

@zzzzBov OK, if we were able to write Hello, World!, I could write a 0 byte program in stuck that does this

@VFDan, the standard loopholes apply.

@zzzzBov IK, but Stuck was not designed to be a language that just prints Hello, World!. It actually is a legitimate programming language, just made for golfing

Is it okay to use "0" instead of 0 (i.e. can I use 0 as a string)?

@zzzzBov In Rust it is not possible to print without a string literal to format the output, like println!("{}", a); prints the value of a. Does this mean that the language is banned unless a workaround can be found?

Windows PowerShell, way too much
Yes, indeed, back in the day we had to write a »Hello world« using (almost exclusively) zeroes ...
&{-join[char[]]($args|% Length)} `
O00000000000000000000000000000000000000000000000000000000000000000000000 `
O0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 `
O00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 `
O00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 `
O00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 `
O0000000000000000000000000000000 `
O00000000000000000000000000000000000000000000000000000000000000000000000000000000000000 `
O00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 `
O00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 `
O00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 `
O000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 `
O00000000000000000000000000000000

On a more serious note:
Windows PowerShell, 25
Write-Host Hello World!

No string literal. The Hello World! in there just happens to be parsed as a string since PowerShell is in argument parsing mode there.

How is that real?? O_o

I searched the internet for some examples or history of this. This is so weird. Could you provide any links?

"Back in the day". :) You millennials crack me up

Oh. Unary. I get it.

C, 327 chars
#define O(O)-~O
#define OO(o)O(O(o))
#define Oo(o)OO(OO(o))
#define oO(o)Oo(Oo(o))
#define oo(o)oO(oO(o))
#define O0 putchar
main() {
    O0(OO(oO(!O0(~O(Oo(OO(-O0(~O(Oo(-O0(O(OO(O0(oo(oO(O0(O(oo(oO(OO(Oo(oo(oO(
    O0(oo(oo(!O0(O(OO(O0(O0(O(OO(Oo(O0(O(Oo(oo(oO(O0(oo(oo(oO(oo(oo(0))))))))
    ))))))))))))))))))))))))))))))))))))));
}

Strangely, it does't lose its beauty after preprocessing:
main() {
putchar(-~-~-~-~-~-~-~-~-~-~!putchar(~-~-~-~-~-~-~-~-putchar(~-~-~-~-~-~-
putchar(-~-~-~putchar(-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~putchar(
-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~
-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~putchar(-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~
-~-~-~-~-~-~-~-~-~-~-~-~-~!putchar(-~-~-~putchar(putchar(-~-~-~-~-~-~-~putchar
(-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~putchar(-~-~-~-~-~-
~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-
~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~-~0))))))))))));
}

Awesome. Missing the !, though.

This is real art!

I feel like the body could be shortened with even more preprocessors. Not sure if the code as a whole would benefeit though.

@Zwei, It's certainly possible to shorten it. I made no effort to find the optimal set of macros.

Why don't you include the parens in the CLANG #define? would save a few bytes, no? Edit: nevermind, just tried and now I see why that won't work ahaha

BrainFuck, 102 111 characters
++++++++[>++++[>++>+++>+++>+<<<<-]>+>->+>>+[<]<-]>>.>>---.+++++++..+++.>.<<-.>.+++.------.--------.>+.

Meets all of the rules.
Credit goes to Daniel Cristofani.

I can't decide if the rules should also state 0 and/or "O" must be used. It's a little mean to BrainFuck and golfscript, but they don't exactly have a hard time with this challenge.

@zzzzBov: If they must be used, then Brainfuck code will just include them. They don't affect the program at all, though.

C, 182 bytes
#define decode(c,o,d,e,g,O,l,f) e##c##d##o
#define HelloWorld decode(a,n,i,m,a,t,e,d)
#define Puzzles(flog) #flog
#define CodeGolf Puzzles(Hello World!)
HelloWorld(){puts(CodeGolf);}

+1,Lol,You still using the token pasting operator trick! Nice mate :-)

C program - 45
(cheating)
Lexically, this doesn't use any string literals or regex literals.  It takes advantage of the stringification feature of the C preprocessor.  s(x) is a macro that turns its argument into a string.
#define s(x)#x
main(){puts(s(Hello World!));}

For a very convenient notion of "lexically" :) But cheekiness FTW!

Unary, 10197 1137672766964589547169964037018563746793726105983919528073581559828 bytes
I'm surprised that no one's done this yet...
It's too long to post here, but it's 1137672766964589547169964037018563746793726105983919528073581559828 zeroes.
Or, more easily read: ~1067 zeroes.
Thanks to @dzaima for saving 10197 bytes

When I read "I once wrote an entire database using only zeroes", my first thought was "he must have done it in unary". +1 for being the only answer to work exactly how the comic did

Haskell - 143 characters
o%y=o.o.o$y;o&y=(o%)%y;o!y=o$o$(o%)&y
r=succ;w=pred;a=r%y;e=r$w&l;l=r!'O';o=r e;u=(w&)&a;y=r%l
main=putStrLn[w!o,o,l,l,y,w u,w$r&'O',y,a,l,e,u]

oy, that was woolly!
No numbers, no numeric operations, variables renamed for amusement.
Some exposition might be nice:

o%y, o&y, and o!y each applies the function o to y multiple times: 3, 9, and 29 times respectively. 29?!?! Yes, 29!
r and w are next and previous character, which when applied using the above higher- order functions can be made to get all the characters needed from 'O'.

The sequence of jumps needed is:
'O' +29    -> 'l'
'O'  +9 -1 -> 'W'
'l'  -9 +1 -> 'd'
'l'  +3    -> 'o'
'd'  +1    -> 'e'
'o'  +3    -> 'r'
'e' -29    -> 'H'
'r' -81    -> '!'
'!'  -1    -> ' '

Edit: (134 -> 144) Forgot to output an exclamation point, sigh....
Edit: (144 -> 143) Removed a unnecessary $, renamed # to ! for Hugs.

o rly? o.o ....

It doesn't work. http://codepad.org/lyKyj1Ox

@Nyuszika7H That's because this service turns on some compiler options by default. It should compile with plain GHC.

@Nyuszika7H It works just fine with GHC. The problem is that that service is using Hugs from 2006. There appear to be two things that Hugs can't deal with: 1) Using '#' as an operator. Changing to '!' makes it work. 2) The definitions of r=succ and w=pred run afoul of how Hugs implements the monomorphism restriction. Changing to r x=succ x and w x=pred x makes it work (at the cost of 4 characters). These seem to be problems in Hugs.

Is it still valid after the @Community edit?

+1, I can confirm this works.

Uhh, r=succ?!

Mathematica 12 chars
Only symbols, no strings.
Hello World!

The ! is a factorial operator, but as the symbols Hello and World are undefined, returns the input unchanged.
If we modify the program a bit:
Hello=2;
World=3;
Hello World!

Then it prints 12 (2 * 3!)

i386 assembly (Linux, gcc syntax), 440 442 435
Today's my assembly day, and after that I'll have had enough for a while.  I allowed myself number 128, see below program for discussion of why.  Nothing extraordinary: I'm just encoding "Hello World!" as assembly opcodes where that made sense without numeric constants, and filled in the rest with arithmetic.
#define M mov
M $0,%ecx;inc %cx;M %ecx,%ebx;inc %cx;M %ecx,%eax;add %ax,%ax
M %ecx,%edx;shl %cl,%dx;M (e),%ch;add %dl,%ch;dec %ch;M %ch,(l)
M %ch,(j);M %ch,(z);M $0,%ch;shl %cl,%edx;M %dl,(s);inc %dl
M %dl,(b);M (o),%dl;M %dl,(u);add %al,%dl;dec %dl;M %dl,(r)
M $m,%ecx;M $n,%edx;int $c;M %ebx,%eax;M $0,%ebx;int $c
.data
m:dec %eax;e:gs;l:es;j:es;o:outsl (%esi),(%dx)
s:es;push %edi;u:es;r:es;z:es;fs;b:es;n=.-m
t=(n+n)/n;c=t<<(t*t+t)

(assemble with gcc -nostartfiles hello.S -o hello, possibly -m32 depending on your arch)
Why the tolerance for  128?  I need syscalls to actually show anything; Linux syscalls are on INT 80h (128 decimal); the only operand format for INT is immediate, so it's not possible to have anything else than a constant (to the code) there.  I could (after I get sober) attempt to express it as a function of other symbolic constants in the code, likely n, but that's getting very boring for not much gain.  I read the constraint on numbers as a way to prevent ASCII coding, and that's definitely not what I'm doing here, so I feel innocent enough to submit this.  (FWIW, I also tried self-modifying code, but that segfaulted)  There's now no 128 left either.  The code's pure!

Edit1 reformatted to save lines; removed a numeric 1 (nobody
noticed?!)
Edit2 compressed mov with CPP macros; eliminated the remaining 128.

This is how real men program.

Javascript - 305
A bit long but I like the method used.
O=0;O++;O=O.toString();alert([O+0+0+O+0+0+0,0+O+O+0+0+O+0+O,O+O+0+O+O+0+0,O+O+0+O+O+0+0,O+O+0+O+O+O+O,O+0+0+0+0+0,O+0+O+0+O+O+O,O+O+0+O+O+O+O, O+O+O+0+0+O+0,O+O+0+O+O+0+0,O+O+0+0+O+0+0,O+0+0+0+0+O].map(function(e){O=0;O++;O++;return String.fromCharCode(parseInt(e,O))}).reduce(function (a,b){return a+b}))

I like it. It would be better with function parameters as OO, OOO, but of course that would make it longer.

Really nice. Does the ',new String()' need to be there at the end? It seems to work without it.

Ah, no it doesn't. Sometimes I forget just how weakly typed Javascript is.

You don't need left 0 bits ('0+') either, and the space and the exclamation have two left 0 bits. Total reduction of 28 characters.

C# (131 chars)
141 chars 142 chars
enum X{Hello,World,A,B=A<<A<<A}class Y{static void Main(){var c=(char)X.B;System.Console.Write(X.Hello.ToString()+c+++X.World+c);}}

Readable:
// Define some constants (B = 32)
enum X { Hello, World, A, B = A << A << A }
class Y
{
    static void Main()
    {
        // Generate the space (character #32)
        var c = (char) X.B;

        // Remember that “!” is character #33
        System.Console.Write(X.Hello.ToString() + c++ + X.World + c);
    }
}

this is twisted and nice. I love it.

+1 nice way to generate certain numbers. Gotta remember that!

LINQPad program, 102 chars: enum X{Hello,World,A,B=A<<A< +"" saves some cahrs

@Firo: ... and breaks the rules. (No string literals allowed.)

79 chars with new Program.cs capabilities:
var c=(char)X.B;Console.Write(X.H.ToString()+c+++X.W+c);enum X{H,W,A,B=A<<A<<A}

JavaScript, 88
t=!0<<-~-~-~-~!0
r=[]
for(i in{Hello:"O",World:0})r+=i+String.fromCharCode(t++)
alert(r)

99
Many thanks to @Timwi for the suggestions
removed ternary operator:
o={Hello:"O",World:0}
t=!0<<-~-~-~-~!0
c=String.fromCharCode
r=c(0)
for(i in o)r+=i+c(t++)
alert(r)

103
aliased String.fromCharCode
o={Hello:"O",World:0}
t=!0<<-~-~-~-~!0
c=String.fromCharCode
for(i in o)o[i]?r=i+c(t):alert(r+i+c(++t))

117
Switched if-else to ternary operator
o={Hello:"O",World:0},t=!0<<-~-~-~-~!0
for(i in o)o[i]?r=i+String.fromCharCode(t):alert(r+i+String.fromCharCode(++t))

125
I'm keeping the "O" just to have an "O" in the program.
o={Hello:"O",World:0},t=!0<<-~-~-~-~!0
for(i in o)if(o[i])r=i+String.fromCharCode(t)
else alert(r+i+String.fromCharCode(++t))

133
o={Hello:"O",World:0},t=!0<<(!0+!0<<!0)+!0
for(i in o)if(o[i])r=i+String.fromCharCode(t)
else r+=i+String.fromCharCode(t+!0)
alert(r)

@Joey, that's largely the point.

@Joey, i read on the codegolf meta that one should avoid answering their own question for some time to encourage others to try various different approaches. My plan was to uncomment it in a day or two.

@Joey, wasn't working on my own machine at the time, and I didn't feel like e-mailing myself the answer when I could just post it in a comment.

@Joey: "There are only five of those" is wrong.  Anyone can suggest an edit.  Just click on "edit" between "link" and "flag" and you can see the code.

@zzz: "that's largely the point"  Anyone can still see it.  Anyone can suggest an edit by clicking on "edit" in between "link" and "flag", which will bring up the edit dialog, revealing your code.

@John: eep, didn't think of that. Sorry then

Now this answer alone is missing the "edit" link when it wasn't ~2 hours ago... what happened?

@John "Anyone can still see it" i understand that, that's why i had it up. If you were interested in looking, you could look, if you were interested in coming up with your own answer, you could come up with your own. I didn't want it visible initially so that people wouldn't just mimic the first thing they saw.

@zzz: Gotcha.  Good plan.

I just discovered the codegolf power of ~- and -~ on numeric literals.

whoops! fixed it.

@zzzzBov Save a Character (and make the character count less unsympathetic :) t=-~!0,t=t<<t*t

Brainfuck, 111 bytes
++++++++++[>+++++++>++++++++++>+++>+<<<<-]>++
.>+.+++++++..+++.>++.<<+++++++++++++++.>.+++.
------.--------.>+.>.

Algorithm explained
Increment cell 0 to 10 (it will be loop counter)
Repeat 10 times ; will stop at cell 0
  Increment cell 1 to 7
  Increment cell 2 to 10
  Increment cell 3 to 3
  Increment cell 4 to 1
Increment cell 1 by 2 and output it ; Thus, output ASCII 72 'H'
etc. for all symbols in 'Hello World!'

Longer version without loop, 389 bytes:
+++++++++++++++++++++++++++++++++++++++++++++
+++++++++++++++++++++++++++.+++++++++++++++++
++++++++++++.+++++++..+++.-------------------
---------------------------------------------
---------------.+++++++++++++++++++++++++++++
++++++++++++++++++++++++++.++++++++++++++++++
++++++.+++.------.--------.------------------
---------------------------------------------
----.-----------------------.

GolfScript, 63 chars
[0))):O.)?O.*-.O.?+)).O.*+((..O+.O(.O+?.O-O*@.O+O.+$.O.*-).O/]+

What, no GolfScript entry yet?
This one uses a single numeric literal 0 and a variable named O (which is used to store the number 3).  Everything else is arithmetic and stack manipulation.  The string Hello World! is built up from its ASCII codes, character by character.
Here's how it works:
[             # insert start-of-array marker
  0))):O      # increment 0 thrice to get 3, and save it in the variable O
  .)?O.*-     # calculate 3^(3+1) - 3*3 = 81 - 9 = 72 = "H"
  .O.?+))     # calculate 72 + 3^3 + 1 + 1 = 72 + 27 + 2 = 101 = "e"
  .O.*+((     # calculate 101 + 3*3 - 1 - 1 = 101 + 9 - 2 = 108 = "l"
  .           # ...and duplicate it for another "l"
  .O+         # calculate 108 + 3 = 111 = "o"
  .           # ...and duplicate it for later use
  O(.O+?      # calculate (3-1)^(3-1+3) = 2^5 = 32 = " "
  .O-O*       # calculate (32 - 3) * 3 = 29 * 3 = 87 = "W"
  @           # pull the second 111 = "o" to the top of the stack
  .O+         # calculate 111 + 3 = 114 = "r"
  O.+$        # copy the (3+3 = 6)th last element on the stack, 108 = "l", to top
  .O.*-)      # calculate 108 - (3*3) + 1 = 108 - 9 + 1 = 100 = "d"
  .O/         # calculate int(100 / 3) = 33 = "!"
]             # collect everything after the [ into an array
+             # stringify the array by appending it to the input string

Python (126 130)
O=ord("O")
N=O/O
T=N+N
R=N+T
E=T**R
E<<T
print'O'[0].join(chr(c+O)for c in[N-E,E*R-T,_-R,_-R,_,N-_-E-E,E,_,_+R,_-R,E*R-R,T-_-E-E])

The literal '' is not allowed.

@romkyns: Very true, fixed.

Not fixed (wrong output). You are probably thinking of [:0].

QR with halfblocks (169) 121 characters
With QR-Code by using UTF-8 Half-blocks characters:
▗▄▄▄▗▄▖▗▄▄▄
▐▗▄▐▝█▙▐▗▄▐
▐▐█▐▝▄ ▐▐█▐
▐▄▄▟▗▗▗▐▄▄▟
▗▗▖▄▞▝ ▗ ▖▄
 ▟▜ Code ▀▟
 ▙▀ Golf ▘▚
▗▄▄▄▐▗▘▟▙▝▝
▐▗▄▐▝▀▛▘▘█▖
▐▐█▐▐▖▐▝▖▜▘
▐▄▄▟▗ ▌█▛▗▝  3

Unfortunely, this won't render nicely there. There is a little snippet with appropriate style sheet, but.. No! The language presented here is not HTML! Language presented here is QR Code! (HTML and CSS is used here only to work around presentation bug!)

 body {
    font-family: monospace;
    line-height:97%;
 }
▗▄▄▄▗▄▖▗▄▄▄

▐▗▄▐▝█▙▐▗▄▐

▐▐█▐▝▄ ▐▐█▐

▐▄▄▟▗▗▗▐▄▄▟

▗▗▖▄▞▝ ▗ ▖▄

 ▟▜ Code ▀▟

 ▙▀ Golf ▘▚

▗▄▄▄▐▗▘▟▙▝▝

▐▗▄▐▝▀▛▘▘█▖

▐▐█▐▐▖▐▝▖▜▘

▐▄▄▟▗ ▌█▛▗▝

QR with halfblocks (169)
  ▛▀▀▌▚▝▐▀▌▛▀▀▌
  ▌█▌▌▖▞▚▚▘▌█▌▌
  ▌▀▘▌ ▚▛▞ ▌▀▘▌
  ▀▀▀▘▚▌▙▘▌▀▀▀▘
  ▄▙▛▚▜▀▄▀█▖▝▄▌
  ▖▄▄▘▖▄▄▄▟▗ ▀▘
  ▜Code  golf!▌
  ▚▟▘▘▝▙▛▚▐▀▖▜▘
  ▘▘ ▀▛▗▚▗▛▀▌▄
  ▛▀▀▌▟▌▜▖▌▘█▐▘
  ▌█▌▌▘█▌▟█▜▙▐
  ▌▀▘▌▚▌▌█▗▝▌▚▘
  ▀▀▀▘ ▝▘▘▀▀▀▀▘

Idealy, this could look like:

Use your smart phone to see this or zbar under linux. (sample: xwd | xwdtopnm | zbarimg /dev/stdin )

Isn't Code golf! a character literal?

No, because it's only there for cosmetic! You could drop and replace them by anything (like ¢@d3||@01f for sample). The number of required characters won't change!

I actually think this answer, though creative, doesn't qualify because it isn't a program. QR is a way to encode data, not a programming language.

Also what about languages like postscript, svg or other presentation languages already used there!? A way to encode is a language anyway... I think!

I don't really know postscript and svg. I think postscript has real programming power - loops and variables - not just encoding. But I wouldn't call a piece of HTML a program (unless it contains JavaScript).

html is not the language, the language is QR! HTML and CSS was usefull to work around presentation bug.

I used HTML (minus JS) as an example for what's not a language. Same goes for QR. See these criteria.

J, 250
oo=:#a.
o0=:<.o.^0
o0o=:%:%:%:oo
ooo=:p:^:(-*oo)
o=:<.(^^^0)*(^^0)*(^^0)
o00=:o,~(,[)o0(**(**[))o0o
oo0=:*/p:(!0),>:p:!0
echo u:(o0(**(**]))o0o),(ooo ooo ooo(o.o.^^^0)*oo),o00,(+:%:oo),(oo0-~!p:>:>:0),o,(<.-:o.o.^o.^0),(>:p:(]^])#o00),(*:#0,#:oo),oo0

I had entirely too much fun with this one, and I learned a little bit more J to boot. Also, ooo ooo ooo may be the stupidest code I've ever written.

ForWhile 22 bytes
!dlroW olleH{}+~(~~@#)
uses ForWhiles ability to read its own source code
online Interpreter
Explanation
! invert empty stack, will push one
dlroW olleH no-ops (all letters and white spaces are interpreted as comments)
{} empty procedure, push current instruction pointer (-14)
+~ add one and flip bits (12 length of the string)
(~~@#) print the first 12 characters of the program (stored at address -1 to -12)

Welcome to Code Golf, and nice answer!

Lua 144 97 86 chars
A different approach, based on the fact that table keys are also strings, and the fact that #Hello == #World == 32 == string.byte'\n'
e=#"O"t=e+e for k,v in pairs{Hello=0,World=e}do T=t^#k io.write(k,string.char(T+v))end

145 char solution

no strings except "O" or 0
no Regexes
no pre-built functions

Did delta encoding of the bytes, then some primenumbers etc etc :)
Golfed version:
e=#"O"d=e+e t=d+e v=d+t z=v+t T=t^d*d^t n=0 for l,m in pairs{T,T/t-z,z,0,d,-T-z,z*z+t*d,T/d,d,-d*t,-t^d,-T+v}do n=n+m io.write(string.char(n))end

Commented:
-- without numbers, strings, regex
-- except "O" and 0
e=#"0"
t=e+e --2
d=t+e -- 3
v=d+t -- 5
z=v+t -- 7
n=0
T=t^d*d^t -- 72 = 2^3+3^2
for l,m in pairs{T, --72
T/t-z, -- 29 = 72/2-7
z, --7
0, -- 0
d, -- 3
-T-z, -- -79 = -72 - 7
z*z+t*d, -- 55 = 7*7 + 2*3
T/d, -- 24 = 72/3
d, -- 3
-d*t, -- -6
-t^d, -- -8
-T+v -- -67 = -72+5
} do
    n=n+q[k]
    io.write(string.char(n))
end

Edit: Changed multiple O strings, and found some more optimalisations.

"O"* - I think the * was for the footnote, not "any number of O's

Well, regex'ing is what I naturally do :p. Could replace it at the cost of 5 or 3 extra characters for respectively the first and second solution

But anyway, I'll edit them out, thanks for the heads up

Hello and World in table constructor are still string literals - that's just a syntatic sugar.

Scala (357 423 361 characters)
Not the shortest answer, unfortunately, but hoping to get bonus marks for the most use of 'O' and '0'
def h(){type t=scala.Char;def OO(c:t)={(c-('O'/'O')).toChar};def O(c:t)={OO(OO(OO(c)))};def O00(c:t)={(c+('O'/'O')).toChar};def O0(c:t)={O00(O00(O00(c)))};val l=O('O');val z=O0(O0(O0(O0(O0(O0(O0(O0(O0(O0(O0(0)))))))))));print(OO(O(O('O'))).toString+(OO(O(O(O('O')))).toString+l+l+'O'+OO(z)+O0(O0(O0(OO('O'))))+'O'+O0('O')+l+OO(OO(O(O(O('O')))))+z).toLowerCase)}

Previously:
def h(){type t=scala.Char;print(OO(O(O('O'))).toString+(OO(O(O(O('O')))).toString+O('O')+O('O')+'O'+OO(O0(O0(O0(O0(O0(O0(O0(O0(O0(O0(O0(0))))))))))))+O0(O0(O0(OO('O'))))+'O'+O0('O')+O('O')+OO(OO(O(O(O('O')))))+O0(O0(O0(O0(O0(O0(O0(O0(O0(O0(O0(0)))))))))))).toLowerCase);def OO[Char](c:t)={(c-('O'/'O')).toChar};def O[Char](c:t)={OO(OO(OO(c)))};def O00[Char](c:t)={(c+('O'/'O')).toChar};def O0[Char](c:t)={O00(O00(O00(c)))}}

Old (illegal) version:
def h(){type t=scala.Char;print(""+OO(O(O('O')))+(""+OO(O(O(O('O'))))+O('O')+O('O')+'O'+OO(O(O(O(O(O('0'))))))+O0(O0(O0(OO('O'))))+'O'+O0('O')+O('O')+OO(OO(O(O(O('O')))))+O(O(O(O(O('0')))))).toLowerCase);def O0[Char](c:t)={O00(O00(O00(c)))};def O[Char](c:t)={OO(OO(OO(c)))};def OO[Char](c:t)={(c-('O'/'O')).toChar};def O00[Char](c:t)={(c+('O'/'O')).toChar}}

I believe the empty string ("") and strings/character literals containing the character zero ('0') are not allowed. Only the string "O" (capital O) and the number 0 are.

Bugger. Some editing required then...

C (or C++) (body segment: 49)
(cheating)
when compiling, compile to a binary called Hello\ World\!, the code is:
#include <stdio.h>
#include <string.h>
int main(int i,char**a)
{
  int j=i+i,k=j<<j;puts(strrchr(*a,'O'-(k<<j))+i);
}

The strrchr segment is required to remove the full path in the event the program name passed in contains the full path, also no arguments must be passed in..
Typical compile line could be: gcc -o Hello\ World\! foo.c

Java 389 characters
spotted a unnecessary declaration
class A{static int a=0,b=a++,f=a,e=a++;static char p(String s){return(char)Byte.parseByte(s,a);}public static void main(String[]z){long x=e,y=b;String c=((Long)x).toString(),d=((Long)y).toString();char l=p(c+c+d+c+c+d+d),m=p(c+c+d+d+c+d+c),o=(char)(l+a+f),_=p(c+d+d+d+d+d),$=_++;System.out.print(new char[]{p(c+d+d+c+d+d+d),m,l,l,o,$,p(c+d+c+d+c+c+c),o,(char)(o+a+f),l,(char)(m-f),_});}}

History is in edit history
now the original ungolfed version readable:
// H  e  l    l   o      W  o  r   l    d  !
//72,101,108,108,111,32,87,111,114,108,100 33
import static java.lang.Integer.*;
class A
{

    public static void main(String[] args)
    {
        Integer a=0,b=a++,e=a++;  // making a 0 a 1 and a 2 which is required later;
        String c=e.toString(),d=b.toString(),z=c.substring(0,0);  //

        String H = ((char)parseInt(d+c+d+d+c+d+d+d,a))+z+  // make binary values and then to char
                (char)parseInt(d+c+c+d+d+c+d+c,a)+
                (char)parseInt(d+c+c+d+c+c+d+d,a)+
                (char)parseInt(d+c+c+d+c+c+d+d,a)+
                (char)parseInt(d+c+c+d+c+c+c+c,a)+
                (char)parseInt(d+d+c+d+d+d+d+d,a)+
                (char)parseInt(d+c+d+c+d+c+c+c,a)+
                (char)parseInt(d+c+c+d+c+c+c+c,a)+
                (char)parseInt(d+c+c+c+d+d+c+d,a)+
                (char)parseInt(d+c+c+d+c+c+d+d,a)+
                (char)parseInt(d+c+c+d+d+c+d+d,a)+
                (char)parseInt(d+d+c+d+d+d+d+c,a)
                ;
        System.out.println(H);  //obvious
    }

C++, 141, 146
First time trying one of these, can probably be improved quite a bit yet:
char o='O'/'O',T=o+o,X=T+o,f=T+X,t=f+f,F=t*f,h=F+F,l=h+t-T,O=l+X;
char c[]={F+t+t+T,h+o,l,l,O,o<<f,h-t-X,O,l+f+o,l,h,0};
cout<<c;

EDIT:
Stole the divide trick from another post, can't believe I didn't think of that :(

You're technically supposed to include the entire working program in the character count, including things like main, any included libraries, std::, etc etc

Haskell - 146
a:b:c:f:g:s:j:z=iterate(\x->x+x)$succ 0
y=[f+j,d+a,c+s+h,l,a+b+l,s,f-s+o,o,a+b+o,l,l-f,a+s]
[h,e,l,_,o,_,w,_,r,_,d,x]=y
main=putStrLn$map toEnum y

I figured pattern matching would give Haskell a huge leg up, in particular because you can initialize powers of two like so:
one:two:four:eight:sixteen:thirty_two:sixty_four:the_rest = iterate (*2) 1

However, as seen in MtnViewMark's Haskell answer (which deserves many many upvotes, by the way) and other answers, better compression can be achieved by using more than just + and -.

C++
/*
Hello World!
*/
#define CodeGolf(r) #r
#include<iostream>
using namespace std;
int main()
{
    char str[*"O"];
    freopen(__FILE__,CodeGolf(r),stdin);
    gets(str);gets(str);puts(str);
}

The 100 violates the rule about numbers.  Please replace it with something more amusing.

@joey-adams Thanks for pointing out. Changed that.

Line 7: error: ISO C++ forbids declaration of 'main' with no type

@george-edison Corrected. Though it worked without int on g++

Clojure - 46 chars
(map print(butlast(rest(str'(Hello World!)))))

Note that Hello and World! are symbols, not literals of any kind.

PHP – 49 chars
<?=Hello.chr(($a=-~-~-~0).~-$a).World.chr($a.$a);

Changelog:

(73 -> 86) Forgot to output an exclamation point... sigh
(86 -> 57) Uses a single variable with incrementing
(57 -> 51) Changed to use bitwise operators on 0
(51 -> 49) More bitwise operators

Pretty sure that the constants would count as string literals because of the conversions.

@Bass5098 Thanks for your edit! I approved it.

@Bass5098 that doesn't work, you need to have chars 32 and 33, not 21 and 22. <?$a=-~-~-~0;echo Hello.chr($a.$a-1).World.chr($a.$a); works, but it's 54 chars.

@zzzzBov I could not figure out how to clear the edit initially, and forgot to roll it back once it was approved.

whoops, i left the 1 in there. There I go breaking my own rules...<?$a=-~-~-~0;echo Hello,chr($a.~-$a),World,chr($a.$a); is what I should have used, still 54 chars.

Even better: <?=Hello.chr(($a=-~-~-~0).~-$a).World.chr($a.$a);, 49 chars.

JavaScript 662 chars
O=[[,],[,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,],[,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,],[,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,],[,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,],[],[,,,,,,,,,,,,,,,,],[,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,],[,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,],[,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,],[,,,,,,,,,,,,,,,,,,,,,,,,,,,,,]];for(O_O=[].length;O.length>O_O;O_O++)document.write(String.fromCharCode((O[O_O].length||-Math.pow([,,].length,[,,,,,].length)-[,,,,,,,].length)+Math.pow([,,].length,[,,,,,,].length)+Math.pow(++[,].length,[,,,].length)-[,].length));document.write(String.fromCharCode(Math.pow([,,].length,[,,,,,].length)+[,].length))

What about abusing array literals just to have unary base. This program has advantage of not using 0.

While this may be valid, this particular puzzle is a code golf, which means you should be aiming for the shortest code possible. At 600+ chars, you're nowhere near the <100 chars that the existing JS solutions already have.

@zzzzBov: I'm actually not trying to win.

This program has advantage of not using 0. What about O_O=0;?

@EriktheGolfer: Fixed, thanks. I failed to notice that one.

O_O=[].length can be written as O_O=false which decreases it by 4.

Python, 106
o=-~-~-~0
L=o+o
d,W=-~L,o**o
_=o*W
print str().join(chr(L+W+_-i)for i in[d*L,L+d,L,L,o,-~_,W,o,0,L,d+d,_])

Use '' (with no preceding space) instead of str()

Also, VERY nice! :)
Btw, the multiple assignment is not saving any characters

@aditsu: I can't, that would be a string literal. Thanks for your comments. :)

Oh oops, somehow the empty string didn't register as a literal in my mind

Perl, 186 bytes
@A=(0,0,0,0);@B=(@A,@A);@C=(@B,@B);@D=(@C,@C);@E=(@D,@D);@d=(@E,@D,@A);$l=[@d,@B];$o=[@$l,0,0,0];print(chr@$_)for[@E,@B],[@d,0],$l,$l,$o,\@D,[@E,@C,@A,0,0,0],$o,[@$o,0,0,0],$l,\@d,[@D,0]

Each chararcter is printed via its ordinal number, which is the length of an array. The construction of the arrays are optimized via the binary representation of the character numbers.
Ungolfed:
@A = (0, 0, 0, 0);          # A = 2^2
@B = (@A, @A);              # B = 2^3
@C = (@B, @B);              # C = 2^4
@D = (@C, @C);              # D = 2^5
@E = (@D, @D);              # E = 2^6

# d = 100 = 0x64 = 1100100b
@d = (@E, @D, @A);          # d = 2^6 + 2^5 + 2^2

# l = 108 = 0x6C = 1101100b
$l = [@d, @B];              # l = d + 2^3

# o = 111 = 0x6F = 1101111b
$o = [@$l, 0, 0, 0];        # o = l + 3

print (chr @$_) for
    [@E, @B],              # "H"    H  =  72 = 0x48 = 1001000b = 2^6 + 2^3
    [@d, 0],               # "e"    e  = 101 = 0x65 = 1100101b = d + 1
    $l, $l, $o,            # "llo"
    \@D,                   # " "   ' ' =  32 = 0x20 = 0100000b = 2^5
    [@E, @C, @A, 0, 0, 0], # "W"    W  =  87 = 0x57 = 1010111b = 2^6 + 2^4 + 2^2 + 3
    $o,                    # "o"
    [@$o, 0, 0, 0],        # "r"    r  = 114 = 0x72 = 1110010b = o + 3
    $l, \@d,               # "ld"
    [@D,0]                 # "!"    !  =  33 = 0x21 = 0100001b = 2^5 + 1

seems that my binary vodoo inspired you :) +1

Perl 6, 199 bytes
my \O=+[0];my \t=O+O;my \T=t+O;my \f=(t+t,O);my \F=t+T;my \S=T+T;my \L=(S,F);
say [~] ((S,T),(|L,t,0),(my \l=(|L,T,t)),l,(my \o=(|l,O,0)),F,(S,|f,t,0),o,(|L,|f),l,(|L,t),(F,0),)
.map({chr [+] t X**@_})

(newlines are added to reduce width, but are unnecessary so are not counted)

Hello World! is encoded as a list of lists of the powers of 2 of each letter.
There is exactly one place where I have a literal 0 that is used for anything other than a 0. It is used to create a one-element list, which is immediately turned into the number 1 with the numeric prefix operator (+[0]).
my \O=+[0];    # one          # (List.elems)
my \t=O+O;     # two
my \T=t+O;     # Three
my \f=(t+t,O); # (four, one)  # <W r>
my \F=t+T;     # five
my \S=T+T;     # six

my \L=(S,F);   # lowercase letter  # (6,5)

say [~] (
  (S,T),            # H
  (|L,t,0),         # e
  (my \l=(|L,T,t)), # l
  l,                # l  reuse <l>
  (my \o=(|l,O,0)), # o  reuse <l>, add 0,1
  F,                # ␠
  (S,|f,t,0),       # W
  o,                # o  reuse <o>
  (|L,|f),          # r
  l,                # l  reuse <l>
  (|L,t),           # d
  (F,0),            # !
).map({chr [+] t X**@_})

Commodore 64 O.0! interpreter

The best I could come up with was to write an interpreter that would accept O and 0 - O starts the counter from 65 (A) and 0 adds 1 to the counter, so you have to enter the following to produce HELLOWORLD**
O0000000O0000O00000000000O00000000000O00000000000000O0000000000000000000000O00000000000000O00000000000000000O00000000000O000

Which I work out at 124 characters. To use, run the program and start typing with O, enter 0 to increase the character count and begin a new character with O again.
** The current version of the interpreter does not support the space or new line character, and you have to break [RUN/STOP] to stop it

APL (Dyalog Unicode), 35 bytesSBCS
{⍞←⍺,⍵,⍨⊃⍕⍬⋄⍞←!}/⎕NL≡Hello World←⍬0

Try it online!
⍬0 the list [[];0]
Hello World← store those two values in these two variables
≡ the depth of that array; ¯2 (max-depth is 2, negative means ragged)
⎕NL Name List of defined variables (class 2 — negative means return as list of strings)
{…}/ apply the following anonymous lambda infix between the two names:
 ⍬ empty list; []
 ⍕ stringify; ""
 ⊃ coerce the first character; " "
 ⍵,⍨ append the right argument; " World"
 ⍺, prepend the left argument; "Hello World"
 ⍞← print that to stdout with no trailing line break
 ⋄ then:
 ⍞←! print the factorial function to stdout

Julia 1.0, 45 bytes
print(string(:([Hello World!]))[-~-~0:~-end])

Try it online!
This is not cheating (I think)

:(...) is an Expr, which represents Julia code (AST or something)
[Hello World!] is a 2 by 1 Matrix containing two variables Hello and World!. They don't need to be defined since they are in an Expr (internally stored as Symbols)
string turns the Expr into a string: "[Hello World!]"
we remove the brackets: -~-~0 is 2 and ~-end is end-1

PHP, 220 202 201 characters
<?$b=++$a+$a;$y=$b+$a;$c=$y+$b;$z=$c*$b;$s=$y*$z+$b;$h=$s*$b+$z-$b;$e=$z*$z+$a;$o=$e+$z;$l=chr($o-$y);echo chr($h).chr($e).$l.$l.chr($o).chr($s).chr($h+$z+$c).chr($o).chr($o+$y).$l.chr(--$e).chr(++$s);

Uses no numbers, string literals, RegEx literals, or pre-built functions that display "Hello World!".
It works: http://codepad.viper-7.com/OhXBkA

Heres my Perl entry.
It uses the length of an array to store the ordinal of the character.
use strict;
use warnings;
use 5.010;
my @hello_world = (
  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
);
say map{ chr @$_ } @hello_world;

That seemed like a lot of writing to me, so I used this to generate the above code:
perl -E'
  say for map{"use $_;"} qw"strict warnings 5.010";
  say "my \@hello_world = (";
  say "  [",join(",",@$_),"]," for map{[(0) x ord]} split //, "Hello World";
  say ");";
  say q"say map{ chr @$_ } @hello_world;"
'

Python (169) -- FIXED
Quite a bit longer than the other solutions. But more insane.
from turtle import setworldcoordinates as w
o=0**0
t=o+o+o
b=cmp.__ne__.__doc__
print(hex.__name__[0]+str(Ellipsis)[:t]+"O"+b[-t*t-o]+w.func_name[t:t*t-o]+b[-t]).title()

Sorry, typo on my behalf. I've corrected that error now.

Nice. I would retract my downvote, but this stupid website doesn’t let me, so don’t blame me...

@Timwi: I think if a question/answer is edited, you can undo your vote, can't you?

C - 125 128 chars
I didn't see a proper C entry so I wrote this one:
main(){char u='O'/'O',t=u+u+u,h=u<<t,s=h<<u+u,d='O'*'O'+t,l=d+h,o='O'|s,
g['O']={'O'-h+u,d+u,l,l,o,s,o+h,o,o+t,l,d,s+u};puts(g);}

(As noted below, redefining u via main(u) can save another 9 bytes.)

Your array isn't NULL-terminated, so it prints junk. Pay 2 chars. Earn them back, and more, by main(u) instead of 'O'/'O'.

C, 190 189 204
a,b,c,h,e,l,o;i[4],*j=i;main(_){o=*"O";a=_+_+_;b=_<>_)^o;o^=c;e=h-a;l=o-h+e;*j++=h-c|e<<b|l<<b+b|l<<c-b;*j++=o|c<<b|o+b-c<<b+b|o<<c-b;*j=o+a|l<<b|e-_<<b+b|c+_<<c-b;puts(i);}

Must be run with exactly zero command line arguments since it depends on argc being equal to 1.
no preprocessor macros
Might be system endian dependant (involves cast from integer array to char array)
Not memory safe

a,b,c,h,e,l,o;   // variables
i[],m,*j=i;      // array and pointer

main(_)          // if no arguments are given _ will be 1
{
    o=*"O";      // our one legal string constant
    a=_+_+_;     // a = 3
    b=_<>_)^o;  // h = 'h'
    o^=c;        // o = 'o'
    e=h-a;       // e = 'e'
    l=o-h+e;     // l = 'l'
    *j++=h-c|e<<b|l<<b+b|l<<c-b;     // j[0] = 'H' | 'e' << 8 | 'l' << 16 | 'l' << 24
    *j++=o|c<<b|o+b-c<<b+b|o<<c-b;   // j[1] = 'o' | ' ' << 8 | 'W' << 16 | 'o' << 24
    *j=o+a|l<<b|e-_<<b+b|c+_<<c-b;   // j[2] = 'r' | 'l' << 8 | 'd' << 16 | '!' << 24

    puts(i);     // puts("Hello World!\0\0\0\0")
}

Revisions:
a,b,c,h,e,l,o;i[9],*j=i;main(_){o=*"O";a=_<<_|_;b=_<<a;c=_<>_)^o;o^=c;e=h-a;l=o-h+e;*j++=h^c|e<<b|l<<b<<b|l<<(c-b);*j++=o|c<<b|(o+b^c)<<b<<b|o<<(c-b);*j=o+a|l<<b|e-_<<b<<b|c+_<<(c-b);printf(i);} /* original */
a,b,c,h,e,l,o;i[4],*j=i;main(_){o=*"O";a=_+_+_;b=_<>_)^o;o^=c;e=h-a;l=o-h+e;*j++=h-c|e<<b|l<<b+b|l<<c-b;*j++=o|c<<b|o+b-c<<b+b|o<<c-b;*j=o+a|l<<b|e-_<<b+b|c+_<<c-b;puts(i);} /* golfed better */
a,b,c,h,e,l,o;i[],m,*j=i;main(_){o=*"O";a=_+_+_;b=_<>_)^o;o^=c;e=h-a;l=o-h+e;*j++=h-c|e<<b|l<<b+b|l<<c-b;*j++=o|c<<b|o+b-c<<b+b|o<<c-b;*j=o+a|l<<b|e-_<<b+b|c+_<<c-b;puts(i);} /* removed illegal numeric literal in array size */

i[9] violates the rules.

shoot, it does doesn't it.

i['O'] should be fine. Or i[-~-~-~-~0].

The way that's there works (with the caveat that it starts scribbling over other global variables, but they're not read from again later so I don't care).  I could probably reorder them to specifically take advantage of this behavior and make them only overwrite variables that are from-then-on unused.  Anyway, at this point it contains no numeric literals and I rather like it that way.

JavaScript 100 chars (when all in one line)
Borrowing subtly from zzzzBov -- with regard to the -~ trick, not seen that before :) -- this is another way to source those pesky space and exclamation characters.
Relies on the Function.toString() ability:
c=!0<<-~-~!0;a=[];
for(i in{Hello:0,world:"O"}){a+=i+([]+function(){!0}).charAt(c);c+=c>>!0}
alert(a)

JavaScript 89 chars (when all in one line)
Also zzzzBov could slightly improve the first example by using the fact that arrays in JS collapse down to strings when used in a calculation; oh, and not creating needless vars ;)
t=!0<<-~-~-~-~!0;r=[];for(i in{Hello:"O",World:0})r+=i+String.fromCharCode(t++);alert(r)

Java - 147, no literals
class HelloCWorlds{static{char[]a=HelloCWorlds.class.getName().toCharArray();int
x=a.length,y=a[--x]%x;a[y]/=x/y;a[x]=a[y]--;System.out.print(a);}}

Run it like this (after compiling):
java HelloCWorlds 2>/dev/null

If you don't want to ignore stderr, then add System.exit(0); after the last semicolon. It brings the file size to 162 and makes use of the 0 literal.

Nice trick! Just one thing to mention: not works with OpenJDK. http://pastebin.com/gxE7PrjX

@manatwork Hmm I think it's not about OpenJDK, but about java 6 vs 7

Possible. BTW, I dug out an old “java version "1.4.2_02" Java(TM) 2 Runtime Environment, Standard Edition (build 1.4.2_02-b03)” to test this – also works fine.

Python3, 16 bytes
import __hello__

Note the rule:

pre-built functions that return "Hello World!"

Does not apply since:

That's an import and not a function
It doesn't return anything
It doesn't return the string but simply prints it.

Python 3 – 99 chars
from re import*
c=X+U+L;_=c+M
print(bytes([X+M,-~c,_,_,_-~I,U,X+U+~M,_-~I,c+S-I,_,c,-~U]).decode())

Taking advantage of the fact that the re module uses integers as flags, e.g. re.X is 64.

JavaScript, 661 characters (without "O" or 0)
That's not the shortest, but that was funny to make. I tried to make it without 0 or "O".
I'm not really happy with H and W because it's the only ones which uses non-symbols characters, but that works. If anyone has an idea to do it ...
This is javascript code, tested in firefox 27 scratchpad, and running with Ctrl+I (should I add an alert or console.log ?).
(document+[])[(++[[]+[]][+[]])<<(++[[]+[]][+[]])<<(++[[]+[]][+[]])<<(++[[]+[]][+[]])] // H
+((!!{})+[])[((++[[]+[]][+[]])<<(++[[]+[]][+[]]))+(++[[]+[]][+[]])]                   // e
+([]+(![]))[(++[[]+[]][+[]])<<(++[[]+[]][+[]])]                                       // l
+([]+(![]))[(++[[]+[]][+[]])<<(++[[]+[]][+[]])]                                       // l
+([]+{})[++[[]+[]][+[]]]                                                              // o
+([]+{})[((++[[]+[]][+[]]<<(~!+[]))+[])[(++[[]+[]][+[]])<<(++[[]+[]][+[]])]]          //
+(self+[])[(++[[]+[]][+[]])<<(++[[]+[]][+[]])<<(++[[]+[]][+[]])<<(++[[]+[]][+[]])]    // W
+([]+{})[++[[]+[]][+[]]]                                                              // o
+([]+(!!{}))[++[[]+[]][+[]]]                                                          // r
+([]+(![]))[(++[[]+[]][+[]])<<(++[[]+[]][+[]])]                                       // l
+([][+[]]+[])[(++[[]+[]][+[]])<<(++[[]+[]][+[]])<<(++[[]+[]][+[]])<<(++[[]+[]][+[]])] // d
+((/!/)+[])[++[[]+[]][+[]]]                                                           // !

(the count of 661 of course doesn't include the comments)

I have one in the Obfuscated Hello world task that makes use of assignment. The idea is to use the Function constructor (which is reachable as ""["constructor"]["constructor"]) to allow arbitrary code. You could do something similar perhaps.

bash, 66 characters
66 characters, no new lines
Hello(){ H=$FUNCNAME;};World! (){ echo $H $FUNCNAME;};Hello;World!

Previous version (81 characters), left here because I like the $IFS trick :-)
81 characters, no new lines
Hello(){ H=$FUNCNAME;};World! (){ echo $H${IFS:0:$[0**0]}$FUNCNAME;};Hello;World!

81 as well but with (including) new lines and easier to read
Hello(){ H=$FUNCNAME;}
World! (){ echo $H${IFS:0:$[0**0]}$FUNCNAME;}
Hello;World!

Commented version
Hello(){ H=$FUNCNAME;}                        # set $H to function name ("Hello")
World! (){ echo $H${IFS:0:$[0**0]}$FUNCNAME;} # print $H, first char of $IFS (" ") & "World!"
Hello;World!                                  # run the stuff

(strictly speaking the calculation 0**0 should be indeterminate but it evaluates to 1 :-D)

Python 2, 116
def Hello(n,m,j):print n.func_name,m.func_name+chr(j)
def World():pass
o=-~0;O=o+o;P=O<<O*O;Hello(Hello,World,P+o)

This is the best I can do so far. Hooray, func_name! (I may or may not try this in Befunge as well.)
(Oops, someone already did this better. Upvote that one instead.)

Python, 139 bytes
class World():
 pass
class Hello(World):
 def __init__(self):
  print(self.__class__.__name__, self.__class__.__base__.__name__)
O=Hello()

I think you can remove 2 bytes by cutting out O=

SmileBASIC, 98 bytes (non-competing)
I admit, this answer is cheating. Labels transparently behave as strings when in an expression, but technically they aren't string or character literals, right? If anyone wants to weigh in feel free but I'm convinced a SmileBASIC answer would just amount to abusing PI() or EXP() to compute every character code.
S=VAL(RIGHT$(@32,2))?RIGHT$(@Hello,5)+CHR$(S+LEN(@O0O0O0O0O0O))+CHR$(S)+RIGHT$(@world,5)+CHR$(S+1)

You could easily golf this more, I'm sure.

Unlambda, 37 bytes
Note that Unlambda doesn't have string or integer literals; .a is a function with a two-character name that writes a to standard output; it's not a function . that takes a as argument.
`.!`.d`.l`.r`.o`.W`. `.o`.l`.l`.e`.Hi

Try it online

Forth (gforth), 38 bytes
: f name type ; f Hello space f World!

Try it online!
OR
name World! name Hello type space type

Try it online!
Explanation
Uses the Forth built-in for processing code to convert the next character entered to a string, and then prints it
Code Explanation
: f             \ start a new word definition
  name          \ grabs the next word (space-delimited) from the input/code
  type          \ output the string on top of the stack
;               \ end word definition
f Hello         \ converts and outputs Hello, as name will grab Hello from the input before continuing
space           \ outputs a single space
f World!        \ converts World! to a string and outputs it

Swift, 193 174 172 126 116 102 bytes
enum h{case Hello,World};print(h.Hello,"\(h.World)\(UnicodeScalar("OOOOOOOOOOO".count*"OOO".count)!)")

Ungolfed:
enum HelloWorld {
    case Hello
    case World
}

let exclamationPoint = String(UnicodeScalar(
    String(repeating: "O", count: 11).count
    * String(repeating: "O", count: 3).count
)!)

print(
    HelloWorld.Hello,
    String(describing: HelloWorld.World) + exclamationPoint
)

Let's go through this step by step:
enum HelloWorld {
    case Hello
    case World
}

When converting these cases to Strings (for example, by printing them or using them in a string interpolation), they will evaluate to "Hello" and "World", respectively.
let exclamationPoint = String(UnicodeScalar(
    String(repeating: "O", count: 11).count
    * String(repeating: "O", count: 3).count
)!)

Since we can't use exclamation points in identifiers, we'll have to do something else. The ASCII value of "!" is 33, so creating an 11-character String and a 3-character String and multiplying their count properties will do the job.
print(
    HelloWorld.Hello,
    String(describing: HelloWorld.World) + exclamationPoint
)

The print call here has 2 arguments: HelloWorld.Hello and String(describing: HelloWorld.World) + exclamationPoint, equivalent to "Hello" and "World" + "!".
By default, print separates its arguments with a space. This gives us our final result of "Hello World!". (There's actually a newline at the end because print's default terminator is a newline.)
Extra Notes

I considered using the -~-~-~0 trick I've seen in some other answers, but Swift doesn't let you use multiple unary operators without parentheses (due to its support for custom operators), meaning it's more like -(~(-(~(-(~0))))), which is horribly inefficient.

Python 272 chars
s=ord('O')
a=len('0')
b=a+a
c=b+a
d=c+a
e=d+a
f=e+a
g=f+a
h=g+a
print chr(s-g)+chr(s+g*c+a)+chr(s+g*d+a)+chr(s+g*d+a)+chr(s+h*d)+chr(s-h*f+a)+chr(s+h)+chr(s+h*d)+chr(s+g*e)+chr(s+g*d+a)+chr(s+g*c)+chr(s-h*f+b)

Though I'm surprised no one tried this method
Python 31 chars
f=open(r'/0.O',)
print f.read()

I don't think '0' is valid. I think only 0 and '0' are valid.

Scala 159
val o='O'/'O'
val t=o+o
val d=t+o
val f=t*t
val e=f*t
val l=' '-d
println (List(-e+o,d*e-t,l,l,' ',-'/',e,' ',' '+d,l,(e-1)*d).map(x=>(x+'O').toChar).mkString)

ungolfed:
val one='O'/'O'
val two=one+one
val drei=two+one // tri, three
val four=two*two
val eight=four<<one

val l=' ' - drei
val h=List(-eight+one, four*eight-two, l, l, ' ', -'/'+one, eight, ' ', ' ' + drei, l, (eight-1)*drei)
println (h.map (x=> (x + 'O').toChar).mkString)

Common Lisp, 35
I think nobody tried Common Lisp. Strictly speaking, a symbol is not a string literal, so this is valid:
(print(symbol-name'|Hello World!|))

Second-short if you count the Mathematica one.

Perl, 96 chars
sub AUTOLOAD{my$x++;$y=$x<<$x++;print substr($AUTOLOAD,$x+$y).chr(($x<<$y)+$a++)}
&Hello;&World

It passes the rules!

Groovy, 117
def propertyMissing(p){p}
b="OOOOOOOO"
c={(char)it.size()}
a=b+b+b+b
println(Hello+c(a+b+"OOOO")+c(a)+World+c(a+"O"))

prints
Hello, World!

Lua, 36
print(next{Hello=0},(next{world=0}))

Tcl
In Tcl, everything is a string.
puts Hello\ World!

If you disallow this, then this is the only valid Tcl program that can be written:

PowerShell: 596 382
Started with Joey's idea (Excel counts 1155 characters!) and cut it by about half with some math, then down to a third with some more math and optimization of my own script.
Original: 596 characters:
My first version was fairly similar to the current one in general theory, but a bit simpler in implementation. I just took each character's ASCII code and broke it into two factors, then converted those into strings of zeroes that were as long as the factors, and made PowerShell put them back together. Some numbers were problematic since the smallest factor pairs I could come up with were pretty high - especially 'e', since 101 is prime.
$O=('000000000','00000000'),('00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000','0'),('0000','000000000000000000000000000'),('0000','000000000000000000000000000'),('000','0000000000000000000000000000000000000'),('00000000','0000'),('000','00000000000000000000000000000'),('000','0000000000000000000000000000000000000'),('000000','0000000000000000000'),('0000','000000000000000000000000000'),('0000000000','0000000000'),('000','00000000000');for($0=0;$0-lt$O.Length;$0++){$O[$0]=($O[$0][0].length,$O[$0][1].length)-join'*'|iex}[char[]]$O-join''

Current: 382 characters
The current version includes a few optimizations, and a change to more comfortably suit the spirit of the challenge.

All factor pairs now end up 23 short of their actual target. This makes every element equate to a composite number, greatly reducing the characters required to build all of them. This alone saved about 156 characters.
Used a ForEach-Object loop, via the % alias, instead of for.
Replaced the 1 (though it was defining array indexes, and so not strictly a number or string literal) with '0'.length. This may cost me some characters, but it's relatively small in comparison to the overall length of the script and helps to fit in with the theme a bit better.
Optimized the multiplication routine by using a % loop instead of individually calling out array elements.
Restructured the script so that no defined variables are needed.

-join[char[]](('0000000','0000000'),('000000','0000000000000'),('00000','00000000000000000'),('00000','00000000000000000'),('00000000','00000000000'),('000','000'),('00000000','00000000'),('00000000','00000000000'),('0000000','0000000000000'),('00000','00000000000000000'),('0000000','00000000000'),('00','00000')|%{(($_|%{$_.length})-join'*'|iex)+'00000000000000000000000'.length})

Step-by-step:
-join[char[]](...) will take an array of integers (generated by the script within), convert them to ASCII characters, and put it all together in one string output.
('0000000','0000000'),('000000','0000000000000'),... are pairs of strings of zeroes. Within a pair, the product of each string's length comes 23 short of an ASCII code needed to represent a character in 'Hello World!'.
|%{...} pipes the factor pairs into a ForEach-Object loop.
(($_|%{$_.length})-join'*'|iex) takes the length of each factor in a pair and multiplies them together.
+'00000000000000000000000'.length effectively adds 23 to the product, resulting in our target ASCII code.

Javascript, 186 Bytes
alert("O00O000OO00O0OOO0OO00OO0OO00OO0OOOO0O00000O0O0OOOOO0OOOOOOO00O0OO0OO00OO00O00".replace(/\D/g,-~0).replace(/......./g,function(O){return String.fromCharCode(parseInt(0+O,-~!0));}))

Fish - 270
>"O":l(?!v~~~~~~~lo 00000v |~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ !<lo0000000000000000000v  |0000000 !<lo000lo~~~~~~lo~~~~~~~~lo~~~~~~~~~v;
^        <|000000000000 !<lo0000000l:oo000lo~~~~~~~~~~~~~~~~~^|000000000000000000 !<lo0000000000^  |~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ !<lo;

Using |0000000000 !< to double the number of 0's put onto the stack. It will bounce off the mirror, and then jump past the <.

C# (169)
class HelloOWorld0
{
    public static void Main()
    {
        Console.WriteLine(typeof(HelloOWorld0).Name.Replace('O', (char) ConsoleKey.Spacebar).Replace('0', (char) ConsoleKey.PageUp));
    }
}

Minified:
class HelloOWorld0{public static void Main(){Console.WriteLine(typeof(HelloOWorld0).Name.Replace('O',(char)ConsoleKey.Spacebar).Replace('0',(char) ConsoleKey.PageUp));}}

Ruby, 115 characters
No numbers or string literals whatsoever.
[(s=-(x=(z=[z].size)+y=z+z)+q=x*x+z)*q+y,z+f=q*q,l=f+q-y,l,o=l+x,_=q*x+y,(s+z)*q+s,o,o+x,l,f,_+z].map{|x|$><<x.chr}

Ruby, 110 characters (but less awesome)
This one has a zero. :(
[(s=-(x=(z=-~0)+y=z+z)+q=x*x+z)*q+y,z+f=q*q,l=f+q-y,l,o=l+x,_=q*x+y,(s+z)*q+s,o,o+x,l,f,_+z].map{|x|$><<x.chr}

z=[z].size is brilliant.

Python (99 bytes)
o=-~0
def World():0
def Hello():print Hello.__name__,World.__name__+chr(o+(o<<(o+o+o+o+o)))
Hello()

(similar to my bash version ).
EDIT: Cut another byte by optimising 0**0 to -~0 (== 1), thanks to @kasran for the tip!

-~0 is a shorter way to get 1 than 0**0.

93 bytes

R, 78
paste(deparse(quote(Hello)),paste0(deparse(quote(World)),deparse(quote(`!`))))

Wanton abuse of deparse (which extracts the literal name of an object, i.e. "de-parsing" it, even if that object doesn't exist) and R's name class, which is not a string literal; is.character(quote(Hello)) returns FALSE. Also ! is a function in R, hence the backticks.
But for a (slightly) more honest solution,
R, 391 after removing whitespace
u = !is.na("O")

paste(
  paste0(letters[u+u+u+u+u+u+u+u],
         letters[u+u+u+u+u],
         letters[u+u+u+u+u+u+u+u+u+u+u+u],
         letters[u+u+u+u+u+u+u+u+u+u+u+u],
         letters[u+u+u+u+u+u+u+u+u+u+u+u+u+u+u]),
  paste0(letters[u+u+u+u+u+u+u+u+u+u+u+u+u+u+u+u+u+u+u+u+u+u+u],
         letters[u+u+u+u+u+u+u+u+u+u+u+u+u+u+u],
         letters[u+u+u+u+u+u+u+u+u+u+u+u+u+u+u+u+u+u],
         letters[u+u+u+u+u+u+u+u+u+u+u+u],
         letters[u+u+u+u])
)

In R, there is a built-in object called letters that's, well, a vector of letters. is.na returns FALSE because "O" is not equal to the special value NA, and ! negates the logical (aka Boolean). Then + in R automatically coerces logicals to numerics.

C# (130 chars)
class 聇聤聫聫聮耟聖聮聱聫聣耠{static void Main(){foreach(var c in typeof(聇聤聫聫聮耟聖聮聱聫聣耠).Name)System.Console.Write((char)(c-short.MaxValue));}}

Even though this beats my 131 chars solution, posting this as a separate answer because it works very differently and the other one is more interesting. (And also because the other one is ASCII-only and thus only 131 bytes long.)

Clojure
The stupid simple (22):
(print 'Hello 'World!)

These are technically symbols, not strings.
In the spirit of the puzzle (204):
(apply str(map(comp char(fn f[x](if x(+(#(+ % %)(f(next x)))({\O (inc 0) \0 0} (first x)))0)) reverse str)'[O00O000 OO00O0O OO0OO00 OO0OO00 OO0OOOO O00000 O0O0OOO OO0OOOO OOO00O0 OO0OO00 OO00O00 O0000O]))

No string or character literals were used.

@Mego, the question rules allow many trivial answers like this to be valid.

Ruby, 182 bytes
->{o=?O.ord;o/=o;t=o+o;"O00O000OO00O0OOO0OO00OO0OO00OO0OOOO0O00000O0O0OOOOO0OOOOOOO00O0OO0OO00OO00O000O0000O".tr(?O,o.to_s).chars.each_slice(t+t+t+o).map{|i|i.join.to_i(t).chr}.join}

Lambda function, returns desired value.

Dyalog APL, 115 bytes
Needs ⎕IO←0 which is default on many systems.
Inspiration.
Plain ASCII encoding using 0 for 0 and O for 1.
⎕UCS(⍴⍬⍬)⊥'0O'⍳'OOOOO0OOOOO00OOOOO0OOOOO000000O0O000O0OOO00O0O000OOOO0OO0OO00000O0OOO0000O00O0OO000O'⍴⍨≢¨⎕TS(⎕D,⍬⍬)

⎕UCS Convert Unicode code points to character
(⍴⍬⍬)⊥ base-2 decode of (⍴⍬⍬ is the length of a list of two empty lists, i.e. 2)
'0O'⍳ indices into 0O for each character in
'OOO...00O' the 7×12 character encoded string
⍴⍨ reshaped into a matrix of dimensions
≢¨ the tally of each of
⎕TS(⎕D,⍬⍬) the Time Stamp and the Digits appended with two empty lists
TryAPL online!

J, 134 124 bytes
Thanks to miles for a bugfix!
echo u:#.((+:+:>.^#a:),<.^+:*_)$'0O'i.'O00O000OO00O0OOO0OO00OO0OO00OO0OOOO0O00000O0O0OOOOO0OOOOOOO00O0OO0OO00OO00O000O0000O'

Try it online! This was much easier to write than the below.
Alternatively, no strings, 134 bytes:
echo u:(-:*:>.>:C),(>:*:<.C),A,A,B,(+:+:>.C),(+:*:<.^.A),(<.*:+:^.A),(B=:>:>:>:A),(+:>:>:>:-:A),A,(*:<.C=:%:A),>.*:>:^.A=:+:<.^+:+:#a:

Try it online! This. Was. A. Triumph Pain to write. I should really write a program to help me automate this...

I think _ counts as a number. Another way to get 1 is #a:

@miles True. I'll make the change accordingly.

Shorter 1: ^0

Shouldnt *_ be ^0 too, since _ is a non-zero number?

PHP, 136 bytes
a different approach, inspired by Adám´s APL answer:
for(;$c=[O00O000,OO00O0O,$l=OO0OO00,$l,$o=OO0OOOO,O00000,O0O0OOO,$o,OOO00O0,$l,OO00O00,O0000O][+$i++];)echo chr(bindec(strtr($c,O,!0)));

loops through array of 0O encoded ASCII values to print corresponding characters. Run with -nr.
breakdown

for(;$c=[O00O000,OO00O0O,$l=OO0OO00,$l,$o=OO0OOOO,  // binary ascii codes,
    O00000,O0O0OOO,$o,OOO00O0,$l,OO00O00,O0000O]    // 1 replaced with O
    [+$i++];)           // loop through array
    echo                    // 4. print
        chr(                // 3. convert to character
        bindec(             // 2. convert to decimal
        strtr($c,O,!0)      // 1. replace capital O with 1
    ));

JavaScript (ES5), 79 bytes
b=-~!0;for(c in{Hello:a="",World:b<<=b*b})a+=c+String.fromCharCode(b++);alert(a)

Explanation
Like the other JavaScript answers, this is just a code snippet that alerts the string'Hello World!'.
The first trick is creating an object with the key names Hello and World. These are not string literals, so it obeys the rules. It is not allowed to put the exclamation mark or the space in there, so we get those characters through the second trick.
The second trick is getting the characters through their ASCII value. Sadly, we have to use String.fromCharCode for that, which is really long. Luckily, the space (32) and exclamation mark (33) are right next to each other in the ASCII table, and the character code for the space is a nice power of 2, which is easily obtainable though bitshifting. Getting 32 using only zeroes is a little bit tricky: 32 equals 1 << 5, which is not very golfable, but it also equals 2 << 4 = 2 << 2 * 2. All these two's allow us to assign 2 to a variable, and use that (note that -~!0 equals 2).
The third trick is that we don't need the values in the object we loop over, and you can assign values to variables in the object declaration. This doesn't just save 2 semicolons, but also 2 dummy values, so 4 bytes in total.
JavaScript (ES6) (non-competing), 82 bytes
_=>eval('b=-~!0;for(c in{Hello:a="",World:b<<=b*b})a+=c+String.fromCharCode(b++)')

Explanation
This is a full function with the same body as the competing version, but we use a fat-arrow function with "the eval trick". eval returns the value of the last variable it assigned to, which is a in this case.
This is non-competing since ECMAScript 6 was released in 2015, more than 4 years after this challenge was made.

C, 177 bytes
enum{a,b,c=b+b,d=c*c,e=c*d,f=c*e,g=c*f,h=c*g,i=c*h};x[]={h+e,i-g+d+b,i-g+e+d,i-g+e+d,i-g+f-b,g,h+f+e-b,i-g+f-b,i-f+c,i-g+e+d,i-g+d,g+b,},j=a;main(){for(;j<f-d;putchar(x[j++]));}

Try it online

Lenguage, 12731474882444739483739382239546264946233453512894971245352595483589354073858968246926319892 bytes
It is 12731474882444739483739382239546264946233453512894971245352595483589354073858968246926319892 zeros. Or Os. Both of them if you want. Any character in fact. Thanks Lenguage.
Convert It Online! <-- Conversion from brainfuck Hello World!
Try It Online! <-- brainfuck Hello World! in action

Tcl, 62 bytes
proc Hello\ world! {} {puts {*}[info level 0]}
[Hello\ world!]

Try it online!
proc Hello\ World! is a function with name "Hello world"; [info level 0] gives the funtion name where I am presently now; [Hello\ world!] is a call to the "Hello world" function!

@Johannes Kuhn: I think my solution is farther from a literal than yours!

JavaScript, 166 bytes
(o=-~0,O=o+[],e=O+0,c=e+0,q=O+c,d=c+0,p=e+O+O+O)=>[c+d,q+e+O,a=O+e+q,a,g=O+p+O,d+0+0,e+p,g,O+q+e,a,q+c,d+0+O].map(b=>String.fromCharCode(parseInt(b,o+o))).join([]+[])

I tried to use most circular alphabet as possible for the variable names.

Runic Enchantments, 94 bytes
mmXm-m-FFm-k$Xm+mm,+:m-:k$Fm+k::}$$::,:++k:}$mKymmmm+++k$mmqnmm,-k${${:FFm+k$k$Fmm+Xk$FFmmqnk@

Try it online!
Wouldn't surprise me if there's a shortcut or two I missed to construct the required values in fewer bytes (mmmm+++ is particularly gross), but managing the stack with duplicated values to be used later incurs its own overhead (as does adjusting the IP
s mana value). As such only the o and l in World are utilized this way, as they are constructed in the order lo and required again later in the order ol, so only 6 total bytes are needed to dup and rotate.
The program functions by drawing on the inherent mana of the instruction pointer to generate numerical values, then performing arithmetic operations on that value as necessary to generate the decimal values 72, 101, 108, 111, 32, 87, 114, 100 in order, casting each to char and printing them.
m  -> push current mana value to stack (default 10)
F  -> lower mana value by 1 ("Fizzle")
mK -> increase mana value by 1 (spawns an IP with m mana, costs m-1, then they combine)
X  -> multiply top of stack by 10 (note that this is not a literal value)
k  -> cast top of stack to Char
$  -> print top of stack

In this way the sequence mXm-m- gives the value 80. FFm gives the value 8. 80 - 8 = 72:
mXm-m-FFm-k$ causes H to be printed.

Keg, 14 bytes
Hello World*

TIO

Keg does not have character literals, only instructions that push constants onto the stack, except for \, which pushes the character onto the stack.
This program does not use integers.
There are no built-functions that return the string in Keg.
Keg does not support regex.

Microsoft Excel, 178 131 chars
Uses the following cells:

A1 - =0=0  TRUE. Since we don't need a real "1", we can just abuse coercion.
A2 - =A1+A1  TRUE + TRUE = 2
A3 - =A2+A1  2 + TRUE = 3
A4 - =A3+A1  3 + TRUE = 4
A6 - =A4+A2  4 + 2 = 6
A8 - =A6+A2  6 + 2 = 8
A9 - =A8+A1  8 + TRUE = 9
B8 - =A4&A2  42
B9 - =A3&A3  33
B1 - =PROPER(BASE(A8&0&A2&A9&B8&A2,A2&A6)&" "&BASE(A3&A8&A8&B8&0&A6&A9,B9)&CHAR(B9))  "Hello World!"

5 + 6 * 8 + 79 = 131 chars.
Only a 0 literal was used. Every other value is a reference dependent on that.
Unobfuscated, the formula is
=PROPER(BASE(8029422,26)&" "&BASE(38842069,33)&CHAR(33))

Arturo, 34 bytes
prints['Hello]prints'World print'!

Try it
Using literals (what might be called symbols in most languages) and a symbolLiteral for the !. Luckily they can be printed directly. A minimum of 3 prints must be used to force the correct spacing.

Vyxal 3, 15 bytes
n½hṪṪtm½½htḢh+Ė

Try it Online!
manipulates the alphabet builtins to create the string "kH" which is evaled to "Hello, World!"

Am I missing something? The challenge says not to use Hello World builtins, this is eventually using it, just in a different order than usual

Also, here’s kH in 12: https://vyxal.github.io/latest.html#WyIiLCIiLCJuwr1owr104biiwr3igKbhtLTJvuG5muKAnCIsIiIsIiIsIjMuNC4xIl0= lower is probably possible with a different method

I can look for golfier ways, and I don't see this as cheating since I never actually used a built in for hello world, I just constructed it

in the one i sent earlier, “halve tail” can be “str-last-half”

Ruby 45 chars
p [:Hello,:World!].join :_20[-~0..~0].hex.chr

or :HelloWorld!.to_s.titleize in rails (26 chars)

Since the rules are already being bent I'm pretty sure :"Hello World!" is technically a Symbol literal.

Never mind, added it as my own.

If that is allowed I should just use #| Hello World␤sub h{};say &h.WHY in Perl 6.

If we push the rules quite a bit.
Ruby, 20
puts :"Hello World!"

Technically :"Hello World!" is just the Symbol syntax.

Yeah... you are pushing the rules.

Befunge 98 - 37
:0!g,:0!0!+:::**+`#@_0!+
Hello World!

The Hello World! is not a string literal. It is source code that would actually do something if you run it (I have no idea what it would do). This program works off the idea of a Befunge quine:
:            duplicate number on stack (note that if there is none, then pushes a 0)
0!           push 0 then not it, producing a 1
g            get the character at the location (:,1) (: = number determined by the previous :)
,            print that character
:            duplicate number on stack (same number as first duplicate)
0!0!+:::**+  push the number 10
`            compare the duplicated number with 10, if it is greater than it, push 1, else push 0.
#            jump over the next character, going to the _
_            move right if the number on the top of the stack is 0, otherwise, move left
@            end program
0!           push 0 then not it, producing a 1
+            add it to the counter (number on top of stack)

I'm working on a longer, more interesting version.

C#, 130 characters
A friend of mine came up with this solution, which is one character shorter than my own solution of 131 (but longer if you count bytes).
class 聇聤聫聫聮耟聖聮聱聫聣耠{static void Main(){foreach(var c in typeof(聇聤聫聫聮耟聖聮聱聫聣耠).Name)System.Console.Write((char)(c-short.MaxValue));}}

Readable:
class 聇聤聫聫聮耟聖聮聱聫聣耠
{
    static void Main()
    {
        foreach (var c in typeof(聇聤聫聫聮耟聖聮聱聫聣耠).Name)
            System.Console.Write((char)(c - short.MaxValue));
    }
}

I'm sorry, but counting by bytes is the standard here.

@SuperJedi224: It is now. This answer is quite old.

Rebol (23 chars)
print ['Hello 'World!]

NB. In Rebol these are word literals ('word) which are completely different to string literals ("string"):
>> type? 'Hello
== word!

>> type? "Hello"
== string!

Alternative if you think using word literals is cheating!
print [quote Hello quote World!]

Forth (942)
I'm sure it's not the shortes forth solution... but it's binary!
First 5 lines are driver.
: O0 0 ;
: OO 0 0 INVERT - ;
: 00 SWAP 2 * + ;
: OOOOOOOO EMIT ;
: O CR BYE ;

O0 OO 00 O0 00 O0 00 OO 00 O0 00 O0 00 O0 00  OOOOOOOO
O0 OO 00 OO 00 O0 00 O0 00 OO 00 O0 00 OO 00  OOOOOOOO
O0 OO 00 OO 00 O0 00 OO 00 OO 00 O0 00 O0 00  OOOOOOOO
O0 OO 00 OO 00 O0 00 OO 00 OO 00 O0 00 O0 00  OOOOOOOO
O0 OO 00 OO 00 O0 00 OO 00 OO 00 OO 00 OO 00  OOOOOOOO
O0 O0 00 OO 00 O0 00 O0 00 O0 00 O0 00 O0 00  OOOOOOOO
O0 OO 00 O0 00 OO 00 O0 00 OO 00 OO 00 OO 00  OOOOOOOO
O0 OO 00 OO 00 O0 00 OO 00 OO 00 OO 00 OO 00  OOOOOOOO
O0 OO 00 OO 00 OO 00 O0 00 O0 00 OO 00 O0 00  OOOOOOOO
O0 OO 00 OO 00 O0 00 OO 00 OO 00 O0 00 O0 00  OOOOOOOO
O0 OO 00 OO 00 O0 00 O0 00 OO 00 O0 00 O0 00  OOOOOOOO
O0 O0 00 OO 00 O0 00 O0 00 O0 00 O0 00 OO 00  OOOOOOOO

O

Edit #1: I'm stupid! I had to insert 2 noop instructions to make it look nearly like a real dump of /dev/zero...
: O0 0 ;
: OO 0 0 INVERT - ;
: 00 SWAP 2 * + ;
: OOOOOOOO EMIT ;
: 00000000 ;
: 0O ;
: O CR BYE ;

O0 OO 00 O0  00 O0 00 OO  00000000
00 O0 00 O0  00 O0 00 0O  OOOOOOOO
O0 OO 00 OO  00 O0 00 O0  00000000
00 OO 00 O0  00 OO 00 0O  OOOOOOOO
O0 OO 00 OO  00 O0 00 OO  00000000
00 OO 00 O0  00 O0 00 0O  OOOOOOOO
O0 OO 00 OO  00 O0 00 OO  00000000
00 OO 00 O0  00 O0 00 0O  OOOOOOOO
O0 OO 00 OO  00 O0 00 OO  00000000
00 OO 00 OO  00 OO 00 0O  OOOOOOOO
O0 O0 00 OO  00 O0 00 O0  00000000
00 O0 00 O0  00 O0 00 0O  OOOOOOOO
O0 OO 00 O0  00 OO 00 O0  00000000
00 OO 00 OO  00 OO 00 0O  OOOOOOOO
O0 OO 00 OO  00 O0 00 OO  00000000
00 OO 00 OO  00 OO 00 0O  OOOOOOOO
O0 OO 00 OO  00 OO 00 O0  00000000
00 O0 00 OO  00 O0 00 0O  OOOOOOOO
O0 OO 00 OO  00 O0 00 OO  00000000
00 OO 00 O0  00 O0 00 0O  OOOOOOOO
O0 OO 00 OO  00 O0 00 O0  00000000
00 OO 00 O0  00 O0 00 0O  OOOOOOOO
O0 O0 00 OO  00 O0 00 O0  00000000
00 O0 00 O0  00 OO 00 0O  OOOOOOOO

O

You used a literal 2 in : 00 SWAP 2 * + ;, which is forbidden.

Look at the other solutions. That's driver.

It's still part of your source code? Also, I looked through every solution rated +1 or more, and there are none that contain any number other than 0, like the rules state, with the exception of one answer using it to specific a version of the language, which may or may not be allowed. What you're doing is not allowed.

You are free to ignore my solution.

Also, SWAP 2 * +, could be written as OVER + +.

Python:
print str().join([chr((~0*(~0+~0))**(~0*(~0+~0+~0))*(~0*(~0+~0+~0))**(~0*(~0+~(0)))),
                  chr((~0*(~0+~0))**(~0*(~0+~0))*(~0*(~0+~0+~0+~0+~0))**(~0*(~0+~0))+~0*~0),
                  chr((~0*(~0+~0))**(~0*(~0+~0))*(~0*(~0+~0+~0)**(~0*(~0+~0+~0)))),
                  chr((~0*(~0+~0))**(~0*(~0+~0))*(~0*(~0+~0+~0)**(~0*(~0+~0+~0)))),
                  chr((~0*(~0+~0))**(~0*(~0+~0+~0+~0))*~0*(~0+~0+~0+~0+~0+~0+~0)+~0),
                  chr((~0*(~0+~0))**(~0*(~0+~0+~0+~0+~0))),
                  chr((~0*(~0+~0))**(~0*(~0+~0+~0))*(~0*(~0+~0+~0))*(~0*(~0+~0+~0+~0+~0))+~0),
                  chr((~0*(~0+~0))**(~0*(~0+~0+~0+~0))*~0*(~0+~0+~0+~0+~0+~0+~0)+~0),
                  chr((~0*(~0+~0))**(~0*(~0+~0))*(~0*(~0+~0+~0+~0+~0))**(~0*(~0+~0))+(~0*(~0+~0))**((~0+~0)*(~0+~0))+~0+~0),
                  chr((~0*(~0+~0))**(~0*(~0+~0))*(~0*(~0+~0+~0)**(~0*(~0+~0+~0)))),
                  chr((~0*(~0+~0))**(~0*(~0+~0))*(~0*(~0+~0+~0+~0+~0))**(~0*(~0+~0))),
                  chr((~0*(~0+~0))**(~0*(~0+~0+~0+~0+~0))+~0*~0)
                  ])

Java @230 : Twisting the rules with Enumerator behavior
enum A{Hello,B,C,D,E,F,World;public static void main(String[]z){p(Hello);int b=(B.ordinal()),c=(b<<F.ordinal());p((char)(c|b<<D.ordinal()|b<<(b<<b)));p((char)c++);p(World);p((char)c);}static void p(Object o){System.out.print(o);}}

took me a while to figure the logic out, enums printed act like literals and cn donate numbers at the same time :P

VBScript: 279
o = Asc("O")
n = 0 ^ 0
w = Round(Cos(o) / Sin(o), 0)
r = Cos(0) + Sgn(o) + Exp(0)
u = Fix(Log(o))
v = Left(o, o ^ 0)
e = Int(Sqr(o))

MsgBox Join(Array( _
    Chr(v & w), _
    Chr(n & 0 & n), _
    Chr(n & 0 & e), _
    Chr(n & 0 & e), _
    LCase("O"), _
    Chr(u & u), _
    Chr(r & w), _
    Chr(e & v), _
    Chr(n & n & n), _
    Chr(n & n & u), _
    Chr(n & 0 & e), _
    Chr(n & 0 & 0), _
    Chr(r & r) _
), String(0, "O"))

Strategy

Generate the numbers 1,2,3,4,7, and 8 from "O" and 0 and common functions
Concatenate the numbers together as strings to form ascii values
Put ascii values in an array
Join the array into a string using an empty string (repeat "o" 0 times) as the delimiter
Display!

This golfs down to (a very beatable) 279 by removing underscores, linebreaks, and all spaces except for one to seperate 'msgbox' and 'join' and more to keep &0s from behaving like hex literals
o=Asc("O"):n=0^0:w=Round(Cos(o)/Sin(o),0):r=Cos(0)+Sgn(o)+Exp(0):u=Fix(Log(o)):v=Left(o,o^0):e=Int(Sqr(o)):MsgBox Join(Array(Chr(v&w),Chr(n& 0&n),Chr(n& 0&e),Chr(n& 0&e),LCase("O"),Chr(u&u),Chr(r&w),Chr(e&v),Chr(n&n&n),Chr(n&n&u),Chr(n& 0&e),Chr(n& 0& 0),Chr(r&r)),String(0,"O"))

Javascript - 129 chars
s=[,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,];c=String.fromCharCode;alert(Object.keys({Hello:s,World:s}).join(c(s.length))+c(++s.length));

You can make your code shorter by replacing console.log with alert and by removing the space between : and null. Also, you forgot to add the exclamation mark at the end of the output.

Okay, I've corrected it.

Befunge-98, 120
'O0!::+::+*-++:,0!::+::*:**\::++-++:,0!::+::+*--+:,+:,0!::++++:,'O%+:,\#@_0!\0!::++/0!:++:0\-0!+:0!:+/:0!:++:0!-::0!:++*

One long line of Befunge. Yikes.
This basically just prints "Hello ", loads in a list of offsets, and then runs the Hello-printing bit again with some offsets applied to turn "Hello " into "World!". It can probably be golfed down a bit further with the representations of numbers.
Edit - Removed two extraneous spaces that had snuck in.

Burlesque, 28 bytes
blsq ) {Hello,}m]\[{world!}m]\[ClwD
Hello, world!

Explanation:
{Hello,} is actually a Block containing the commands He, ll and o,.
The reason we can't use {Hello, world!} is because the parser skips whitespaces obviously. m] converts commands to strings and \[ concatenates them. With wD (which is unwords) we insert missing space.
For what it's worth a few notes about how Burlesque parses commands.
Pretty much everything that does not start with a digit will be parsed as a command with the exception of the minus sign which tries to parse a double first, if that fails it tries to parse it as an integer and if that fails it tries to parse it as a command. For example a{b} contains NO block. That's the command a{ followed by the command b}. {ab} is a block that contains the command ab. {-}-}} is a block containing the command -} twice.  a2.0 is the command a2 followed by the command .0. (That 2.0 is NOT a double in there).

Hieroglyphy With 0s, 6129
Golfed down from a generated expression in pure hieroglyphy (itself a variant of the infamous JSF***) which was 7999 bytes long.
Basically exploits the oddities of javascript's type system to generate the string using only the character set [](){}+!0.
[][(![]+[])[!0+!0+!0]+([]+{})[+!0]+(!0+[])[+!0]+(!0+[])[0]][([]+{})[!0+!0+!0+!0+!0]+([]+{})[+!0]+([][0]+[])[+!0]+(![]+[])[!0+!0+!0]+(!0+[])[0]+(!0+[])[+!0]+([][0]+[])[0]+([]+{})[!0+!0+!0+!0+!0]+(!0+[])[0]+([]+{})[+!0]+(!0+[])[+!0]]((!0+[])[+!0]+([][0]+[])[!0+!0+!0]+(!0+[])[0]+([][0]+[])[0]+(!0+[])[+!0]+([][0]+[])[+!0]+([]+{})[!0+!0+!0+!0+!0+!0+!0]+([][0]+[])[0]+([][0]+[])[+!0]+([][0]+[])[!0+!0+!0]+(![]+[])[!0+!0+!0]+([]+{})[!0+!0+!0+!0+!0]+(+{}+[])[+!0]+([]+[][(![]+[])[!0+!0+!0]+([]+{})[+!0]+(!0+[])[+!0]+(!0+[])[0]][([]+{})[!0+!0+!0+!0+!0]+([]+{})[+!0]+([][0]+[])[+!0]+(![]+[])[!0+!0+!0]+(!0+[])[0]+(!0+[])[+!0]+([][0]+[])[0]+([]+{})[!0+!0+!0+!0+!0]+(!0+[])[0]+([]+{})[+!0]+(!0+[])[+!0]]((!0+[])[+!0]+([][0]+[])[!0+!0+!0]+(!0+[])[0]+([][0]+[])[0]+(!0+[])[+!0]+([][0]+[])[+!0]+([]+{})[!0+!0+!0+!0+!0+!0+!0]+(![]+[])[!0+!0]+([]+{})[+!0]+([]+{})[!0+!0+!0+!0+!0]+(+{}+[])[+!0]+(!0+[])[0]+([][0]+[])[!0+!0+!0+!0+!0]+([]+{})[+!0]+([][0]+[])[+!0])())[!0+!0+!0]+([][0]+[])[!0+!0+!0])()([][(![]+[])[!0+!0+!0]+([]+{})[+!0]+(!0+[])[+!0]+(!0+[])[0]][([]+{})[!0+!0+!0+!0+!0]+([]+{})[+!0]+([][0]+[])[+!0]+(![]+[])[!0+!0+!0]+(!0+[])[0]+(!0+[])[+!0]+([][0]+[])[0]+([]+{})[!0+!0+!0+!0+!0]+(!0+[])[0]+([]+{})[+!0]+(!0+[])[+!0]]((!0+[])[+!0]+([][0]+[])[!0+!0+!0]+(!0+[])[0]+([][0]+[])[0]+(!0+[])[+!0]+([][0]+[])[+!0]+([]+{})[!0+!0+!0+!0+!0+!0+!0]+([][0]+[])[!0+!0+!0]+(![]+[])[!0+!0+!0]+([]+{})[!0+!0+!0+!0+!0]+(+{}+[])[+!0]+([]+[][(![]+[])[!0+!0+!0]+([]+{})[+!0]+(!0+[])[+!0]+(!0+[])[0]][([]+{})[!0+!0+!0+!0+!0]+([]+{})[+!0]+([][0]+[])[+!0]+(![]+[])[!0+!0+!0]+(!0+[])[0]+(!0+[])[+!0]+([][0]+[])[0]+([]+{})[!0+!0+!0+!0+!0]+(!0+[])[0]+([]+{})[+!0]+(!0+[])[+!0]]((!0+[])[+!0]+([][0]+[])[!0+!0+!0]+(!0+[])[0]+([][0]+[])[0]+(!0+[])[+!0]+([][0]+[])[+!0]+([]+{})[!0+!0+!0+!0+!0+!0+!0]+(![]+[])[!0+!0]+([]+{})[+!0]+([]+{})[!0+!0+!0+!0+!0]+(+{}+[])[+!0]+(!0+[])[0]+([][0]+[])[!0+!0+!0+!0+!0]+([]+{})[+!0]+([][0]+[])[+!0])())[!0+!0+!0]+([][0]+[])[!0+!0+!0])()(([]+{})[0])[0]+(!0+!0+!0+!0+[])+(!0+!0+!0+!0+!0+!0+!0+!0+[]))+([][0]+[])[!0+!0+!0]+(![]+[])[!0+!0]+(![]+[])[!0+!0]+([]+{})[+!0]+([]+{})[!0+!0+!0+!0+!0+!0+!0]+[][(![]+[])[!0+!0+!0]+([]+{})[+!0]+(!0+[])[+!0]+(!0+[])[0]][([]+{})[!0+!0+!0+!0+!0]+([]+{})[+!0]+([][0]+[])[+!0]+(![]+[])[!0+!0+!0]+(!0+[])[0]+(!0+[])[+!0]+([][0]+[])[0]+([]+{})[!0+!0+!0+!0+!0]+(!0+[])[0]+([]+{})[+!0]+(!0+[])[+!0]]((!0+[])[+!0]+([][0]+[])[!0+!0+!0]+(!0+[])[0]+([][0]+[])[0]+(!0+[])[+!0]+([][0]+[])[+!0]+([]+{})[!0+!0+!0+!0+!0+!0+!0]+([][0]+[])[0]+([][0]+[])[+!0]+([][0]+[])[!0+!0+!0]+(![]+[])[!0+!0+!0]+([]+{})[!0+!0+!0+!0+!0]+(+{}+[])[+!0]+([]+[][(![]+[])[!0+!0+!0]+([]+{})[+!0]+(!0+[])[+!0]+(!0+[])[0]][([]+{})[!0+!0+!0+!0+!0]+([]+{})[+!0]+([][0]+[])[+!0]+(![]+[])[!0+!0+!0]+(!0+[])[0]+(!0+[])[+!0]+([][0]+[])[0]+([]+{})[!0+!0+!0+!0+!0]+(!0+[])[0]+([]+{})[+!0]+(!0+[])[+!0]]((!0+[])[+!0]+([][0]+[])[!0+!0+!0]+(!0+[])[0]+([][0]+[])[0]+(!0+[])[+!0]+([][0]+[])[+!0]+([]+{})[!0+!0+!0+!0+!0+!0+!0]+(![]+[])[!0+!0]+([]+{})[+!0]+([]+{})[!0+!0+!0+!0+!0]+(+{}+[])[+!0]+(!0+[])[0]+([][0]+[])[!0+!0+!0+!0+!0]+([]+{})[+!0]+([][0]+[])[+!0])())[!0+!0+!0]+([][0]+[])[!0+!0+!0])()([][(![]+[])[!0+!0+!0]+([]+{})[+!0]+(!0+[])[+!0]+(!0+[])[0]][([]+{})[!0+!0+!0+!0+!0]+([]+{})[+!0]+([][0]+[])[+!0]+(![]+[])[!0+!0+!0]+(!0+[])[0]+(!0+[])[+!0]+([][0]+[])[0]+([]+{})[!0+!0+!0+!0+!0]+(!0+[])[0]+([]+{})[+!0]+(!0+[])[+!0]]((!0+[])[+!0]+([][0]+[])[!0+!0+!0]+(!0+[])[0]+([][0]+[])[0]+(!0+[])[+!0]+([][0]+[])[+!0]+([]+{})[!0+!0+!0+!0+!0+!0+!0]+([][0]+[])[!0+!0+!0]+(![]+[])[!0+!0+!0]+([]+{})[!0+!0+!0+!0+!0]+(+{}+[])[+!0]+([]+[][(![]+[])[!0+!0+!0]+([]+{})[+!0]+(!0+[])[+!0]+(!0+[])[0]][([]+{})[!0+!0+!0+!0+!0]+([]+{})[+!0]+([][0]+[])[+!0]+(![]+[])[!0+!0+!0]+(!0+[])[0]+(!0+[])[+!0]+([][0]+[])[0]+([]+{})[!0+!0+!0+!0+!0]+(!0+[])[0]+([]+{})[+!0]+(!0+[])[+!0]]((!0+[])[+!0]+([][0]+[])[!0+!0+!0]+(!0+[])[0]+([][0]+[])[0]+(!0+[])[+!0]+([][0]+[])[+!0]+([]+{})[!0+!0+!0+!0+!0+!0+!0]+(![]+[])[!0+!0]+([]+{})[+!0]+([]+{})[!0+!0+!0+!0+!0]+(+{}+[])[+!0]+(!0+[])[0]+([][0]+[])[!0+!0+!0+!0+!0]+([]+{})[+!0]+([][0]+[])[+!0])())[!0+!0+!0]+([][0]+[])[!0+!0+!0])()(([]+{})[0])[0]+(!0+!0+!0+!0+!0+[])+(!0+!0+!0+!0+!0+!0+!0+[]))+([]+{})[+!0]+(!0+[])[+!0]+(![]+[])[!0+!0]+([][0]+[])[!0+!0]+[][(![]+[])[!0+!0+!0]+([]+{})[+!0]+(!0+[])[+!0]+(!0+[])[0]][([]+{})[!0+!0+!0+!0+!0]+([]+{})[+!0]+([][0]+[])[+!0]+(![]+[])[!0+!0+!0]+(!0+[])[0]+(!0+[])[+!0]+([][0]+[])[0]+([]+{})[!0+!0+!0+!0+!0]+(!0+[])[0]+([]+{})[+!0]+(!0+[])[+!0]]((!0+[])[+!0]+([][0]+[])[!0+!0+!0]+(!0+[])[0]+([][0]+[])[0]+(!0+[])[+!0]+([][0]+[])[+!0]+([]+{})[!0+!0+!0+!0+!0+!0+!0]+([][0]+[])[0]+([][0]+[])[+!0]+([][0]+[])[!0+!0+!0]+(![]+[])[!0+!0+!0]+([]+{})[!0+!0+!0+!0+!0]+(+{}+[])[+!0]+([]+[][(![]+[])[!0+!0+!0]+([]+{})[+!0]+(!0+[])[+!0]+(!0+[])[0]][([]+{})[!0+!0+!0+!0+!0]+([]+{})[+!0]+([][0]+[])[+!0]+(![]+[])[!0+!0+!0]+(!0+[])[0]+(!0+[])[+!0]+([][0]+[])[0]+([]+{})[!0+!0+!0+!0+!0]+(!0+[])[0]+([]+{})[+!0]+(!0+[])[+!0]]((!0+[])[+!0]+([][0]+[])[!0+!0+!0]+(!0+[])[0]+([][0]+[])[0]+(!0+[])[+!0]+([][0]+[])[+!0]+([]+{})[!0+!0+!0+!0+!0+!0+!0]+(![]+[])[!0+!0]+([]+{})[+!0]+([]+{})[!0+!0+!0+!0+!0]+(+{}+[])[+!0]+(!0+[])[0]+([][0]+[])[!0+!0+!0+!0+!0]+([]+{})[+!0]+([][0]+[])[+!0])())[!0+!0+!0]+([][0]+[])[!0+!0+!0])()([][(![]+[])[!0+!0+!0]+([]+{})[+!0]+(!0+[])[+!0]+(!0+[])[0]][([]+{})[!0+!0+!0+!0+!0]+([]+{})[+!0]+([][0]+[])[+!0]+(![]+[])[!0+!0+!0]+(!0+[])[0]+(!0+[])[+!0]+([][0]+[])[0]+([]+{})[!0+!0+!0+!0+!0]+(!0+[])[0]+([]+{})[+!0]+(!0+[])[+!0]]((!0+[])[+!0]+([][0]+[])[!0+!0+!0]+(!0+[])[0]+([][0]+[])[0]+(!0+[])[+!0]+([][0]+[])[+!0]+([]+{})[!0+!0+!0+!0+!0+!0+!0]+([][0]+[])[!0+!0+!0]+(![]+[])[!0+!0+!0]+([]+{})[!0+!0+!0+!0+!0]+(+{}+[])[+!0]+([]+[][(![]+[])[!0+!0+!0]+([]+{})[+!0]+(!0+[])[+!0]+(!0+[])[0]][([]+{})[!0+!0+!0+!0+!0]+([]+{})[+!0]+([][0]+[])[+!0]+(![]+[])[!0+!0+!0]+(!0+[])[0]+(!0+[])[+!0]+([][0]+[])[0]+([]+{})[!0+!0+!0+!0+!0]+(!0+[])[0]+([]+{})[+!0]+(!0+[])[+!0]]((!0+[])[+!0]+([][0]+[])[!0+!0+!0]+(!0+[])[0]+([][0]+[])[0]+(!0+[])[+!0]+([][0]+[])[+!0]+([]+{})[!0+!0+!0+!0+!0+!0+!0]+(![]+[])[!0+!0]+([]+{})[+!0]+([]+{})[!0+!0+!0+!0+!0]+(+{}+[])[+!0]+(!0+[])[0]+([][0]+[])[!0+!0+!0+!0+!0]+([]+{})[+!0]+([][0]+[])[+!0])())[!0+!0+!0]+([][0]+[])[!0+!0+!0])()(([]+{})[0])[0]+(!0+!0+[])+(+!0+[]))

Because this "language" is a subset of javascript, you can run this right from your browser console. It returns the string "Hello World!".

Hassium, 264 Bytes
Well this was interesting.
use Math;func main(){a=Math.pi;a/=a;b=a+a;t=Math.pow(b+b,b+a);o=t+Math.pow(b*b+b,b);d(t+(b*b*b));d(o+a);c=o+(b*b*b)d(c)d(c)d(c+b+a)d(Math.pow(b*b,b)*2)d(o-((b*(b*b)+(b*b+a))))d(c+b+a)d((c+b+a)+(b+a))d(c)d(o)d(Math.pow(b*b,b)*b+a);}func d(m)print(Convert.toChar(m))

Run online and see expanded here

Prolog, 198 bytes
p:-atom_codes('O0',[O,N]),A is O-N,B is O/O,C is A-B-B,D is B+B+B,G is O+C,H is G+D,I is H+D,K is A+B,L is K+B,M is C*D,J is L*D+B,F is J+B,E is F-C,atom_codes(X,[E,F,G,G,H,K,M,H,I,G,J,L]),write(X).

Explanation
p:-atom_codes('O0',[O,N]),                      % O=79, N=48
   A is O-N,                                    % A=79-48=31
   B is O/O,                                    % B=79/79=1
   C is A-B-B,                                  % C=31-1-1=29
   D is B+B+B,                                  % D=1+1+1=3
   G is O+C,                                    % G=79+29=108
   H is G+D,                                    % H=108+3=111
   I is H+D,                                    % I=111+3=114
   K is A+B,                                    % K=31+1=32
   L is K+B,                                    % L=32+1=33
   M is C*D,                                    % M=29*3=87
   J is L*D+B,                                  % J=33*3+1=100
   F is J+B,                                    % F=100+1=101
   E is F-C,                                    % E=101-29=72
   atom_codes(X,[E,F,G,G,H,K,M,H,I,G,J,L]),     % X='Hello World!'
   write(X).

Emacs Lisp, 281 bytes
(defalias'O'string-to-char)
(setq O(1+(O"O"))O0(-(1+ O)(O"O"))OO(* O0 O0 O0 O0 O0 O0)O1(+ O(- O OO))OOO(+ O1 (* O0 O0 O0) O0 O0)OO1(1+ (+ OOO O0)))
(princ(string(-O(* O0 O0 O0))(1+(+ O1 O0 O0))OOO OOO OO1 (/ OO O0)(1+ (+ O O0 O0 O0))OO1(1+ (+ OO1 O0))OOO(+ O1 O0 O0)(1+(/ OO O0))))

1+ is not a number, but a function, that returns 1 + NUMBER with NUMBER as its argument.
Ungolfed:
(defalias'O'string-to-char)
(setq O (1+ (O"O"))                 ; 80 => "P"
      O0 (-(1+ O)(O"O"))            ; 2
      OO (* O0 O0 O0 O0 O0 O0)      ; 64
      O1 (+ O(- O OO))              ; 96
      OOO (+ O1 (* O0 O0 O0) O0 O0) ; 108 => "l"
      OO1 (1+ (+ OOO O0)))          ; 111 => "o"
(princ
 (string
  (- O (* O0 O0 O0))   ; "H"
  (1+(+ O1 O0 O0))     ; "e"
  OOO                  ; "l"
  OOO                  ; "l"
  OO1                  ; "o"
  (/ OO O0)            ; " "
  (1+ (+ O O0 O0 O0))  ; "W"
  OO1                  ; "o"
  (1+ (+ OO1 O0))      ; "r"
  OOO                  ; "l"
  (+ O1 O0 O0)         ; "d"
  (1+ (/ OO O0))))     ; "!"

Clojure, 19 bytes
Since I am not allowed to comment (yet) both of atrociously long Clojure answers, here is mine:
(pr 'Hello 'World!)

3 bytes shorter than print

'something is a symbol, not string literal. Symbols evaluate to their names, which are string literals

don't symbols have all caps?

PHP, 160 157 bytes
no literals at all. Still wonder if it has golfing potential left:
for(;$c=[$h=($f=($t=++$n+$n)+$t)+$f+$s=$f*$f*$f,$e=$s+$s/$t+$v=$f+$n--,$l=$e+$f+--$f,$l,$o=$l+$f,$s/=$t,$h+$v*$f,$o,$o+$f,$l,--$e,++$s][+$i++];)echo chr($c);

creates an array with the ascii codes and loops through it to print the characters.
Run with -nr or try it online.
breakdown
for(;$c=[$h=
    ($f=($t=++$n+$n)+$t)    #       $n=1,$t=2,$f=4
    +$f+$s=$f*$f*$f,        # H     $s=64,$h=72
    $e=$s+$s/$t+$v=$f+$n--, # e     $n=0,$v=5,$e=101
    $l=$e+$f+--$f,$l,       # ll    $f=3,$l=108
    $o=$l+$f,               # o     $o=111
    $s/=$t,                 # space $s=32
    $h+$v*$f,$o,            # Wo
    $o+$f,$l,               # rl
    --$e,                   # d     $e=100
    ++$s                    # !     $s=33
][+$i++];)          # loop through array
    echo chr($c);           # print character

ZX Spectrum BASIC, 16 bytes
(including the end of line, but excluding the line number, since that is not part of the code itself)
The hexadecimal representation of the code is:
08 08 48 65 6c 6c 6f 2c 20 77 6f 72 6c 64 21 0d

Its "normal" entry would be:
1\x08\x08Hello, world!

where 1 is the (unimportant) line number, \x08 means byte with the value 0x08 - you might have to overcome some slight difficulties if you want to enter it from the keyboard.
Note that Hello, world! is not a string literal, but part of the code itself.
Bonus: you do not have to RUN the program, just "having" it in the computer is enough (in keyword mode) to display:

If you accept "garbage" around the message, the code could be made shorter by three bytes.

loophole: As "part of the code", it´s a string literal; no matter how you call it. It is also no program, not even a code snippet. It´s actually just plain text.

@Titus No, it most definitely is not a string literal - in ZX Spectrum BASIC there is a very sharp difference between code and literals - numbers and strings (also in how they are represented in RAM). And this is none of them, it's neither a string variable.

F#, 103 bytes
let[<EntryPoint>]``Hello world!``a=System.Reflection.MethodBase.GetCurrentMethod().Name|>stdout.Write;0

Similar to some of the other answers here. The `` characters around the method name are not literals, rather they "delimit an identifier that would otherwise not be a legal identifier, such as a language keyword." (Source)
They do make F# nice for writing tests, since you can give a long human-language name for the tests instead of a programming-language name.

Pascal (FPC), 1245 bytes
it's kinda long and crazy ngl
{$macro on}
{$define _O:=chr(Length(}
{$define O_:=))}

begin
  write(_O'000000000000000000000000000000000000000000000000000000000000000000000000'O_,_O'00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000'O_,_O'000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000'O_,_O'000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000'O_,_O'000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000'O_,_O'00000000000000000000000000000000'O_,_O'000000000000000000000000000000000000000000000000000000000000000000000000000000000000000'O_,_O'000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000'O_,_O'000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000'O_,_O'000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000'O_,_O'0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000'O_,_O'000000000000000000000000000000000'O_);
end.

Try it online!

(,) 375 344 334 Chars or \$334\log_{256}(3)\approx66.17\$ Bytes
(()()(),()()()()()()())((),(()()())()()())((()),(())(())(()))(((())),((()))((()))(()))(,,,(((())))()())(()(),(((())))((()))())(,,,(()()))(,,,(()())(()()()),(),,()())(,,,(()())(()))(,,,((()))(())()()()())(,,,((()))()())(,,,(((())))(())(()()()))(,,,(()())(()))(,,,(()())(())()()())(,,,(()())(()()()))(,,,(((())))((())))(,,,((()))()()())

Same as my normal answer.
Tio

Python, 180 Bytes
f=lambda *a:a[0]
class Hello(metaclass=f):0
class World(metaclass=f):0
print(Hello+chr(len("OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO"))+World+chr(len("OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO")))

Try It Online!
Explanation (might need to scroll)
f=lambda *a:a[0]
class Hello(metaclass=f):0
class World(metaclass=f):0
print(Hello+chr(len("OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO"))+World+chr(len("OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO")))

f=lambda *a:a[0]                                                                                # Make a function that returns the first argument (returns the name of the class when used as a metaclass).
class Hello(metaclass=f):0                                                                                # Use the metaclass function f on the classes Hello and World to get the name of the class when called without brackets.
class World(metaclass=f):0
print(Hello+chr(len("OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO"))+World+chr(len("OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO")))  # Print "Hello World!".
            chr(len("OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO"))                                                       # Space character made from unary.
                                                               chr(len("OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO"))   # Exclamation mark made from unary.

 Created with the help of Luminespire at https://vyxal.github.io/Luminespire

YASEPL, 184 bytes
=O$+^^**++++++++›+++++++++++++++++++++++++++++›+++++++››+++›$+++++++++++**----›------------›*+++++++++++++++++++++++›$+******-----------------›+++›------›--------›$*****+›

char codes my beloved

C# (357)
class H
{
    static void main()
    {
         Func<ConsoleKey, char> f = (k) => (char) k;
         Func<char, char> l = (c) => char.ToLower(c);

         Console.WriteLine(new[] {
             f(ConsoleKey.H),
             l(f(ConsoleKey.E)),
             l(f(ConsoleKey.L)),
             l(f(ConsoleKey.L)),
             l(f(ConsoleKey.O)),
             f(ConsoleKey.Spacebar),
             f(ConsoleKey.W),
             l(f(ConsoleKey.O)),
             l(f(ConsoleKey.R)),
             l(f(ConsoleKey.L)),
             l(f(ConsoleKey.D)),
             f(ConsoleKey.PageUp)
        });
    }
}

Golfed:
class H{static void main(){Func<ConsoleKey,char>f=(k)=>(char)k;Func<char,char>l=(c)=>char.ToLower(c);Console.WriteLine(new[]{f(ConsoleKey.H),l(f(ConsoleKey.E)),l(f(ConsoleKey.L)),l(f(ConsoleKey.L)),l(f(ConsoleKey.O)),f(ConsoleKey.Spacebar),f(ConsoleKey.W),l(f(ConsoleKey.O)),l(f(ConsoleKey.R)),l(f(ConsoleKey.L)),l(f(ConsoleKey.D)),f(ConsoleKey.PageUp)});}}

using C = System.ConsoleKey; would save a number of chars.

I don't think it will.  Enum constants can only be referred through Enum.

Next time, please compile your programs before posting them. This needs a using System and Main needs to be capitalized. However, the suggestion made by @zzzzBov is correct; you can use using C=System.ConsoleKey; to abbreviate the code massively. Furthermore, you can remove the parentheses around the lambda parameters. That takes it down to 275.

Ruby 49 chars
def Hello World!;puts __method__;end
Hello World!

The whitespace in the method name is a UTF8 Emsp, a little wider then a normal space which would be a syntax error.

Windows Batch (17)
Inspired by Joey's answer.
echo Hello World!

Does Hello World! not qualify as a string literal here? Curious.

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text:
The fourth power (Juzuk)
In 1939 Juzuk described a way to generate the fourth powers of natural numbers.
Group the natural numbers like this:
1   2 3   4 5 6   7 8 9 10   11 12 13 14 15   ...

Scratch each second group:
1   4 5 6   11 12 13 14 15 ...

The sum of the n remaining groups is n**4.

Input: none
Task: print the fourth powers upto 100**4, using Juzuk's method.
Output:
0 (optional)
1
16
81
...
100000000

While I find it acceptable to forbid language specificities that make it too easy to solve a problem, I'm not fond of that “use Juzuk’s method” rule. Is it allowed to take the n-1 result in account when computing for n? Is it allowed to simplify integer sums using the n(n+1)/2 formula? When is it no longer Juzuk’s method?

Rhetorical questions?

I’m voting to close this question because "implement Juzuk's algorithm" is an unobservable requirement

J, 40 38 (not summing unneeded)
+/\+/"1(+:i.100){(#~i.201)[/.>:i.20100

J, 30 (summing unneeded)
+/\_2{.\(#~i.201)+//.>:i.20100

J, 33
~.+/\(#~i.200)(+/*2|#)/.1+i.2!200

Summing the groups you'll scratch later is a nice codesize optimization, but in an "implement it this way" context, I feel robbed ;)

@JB: well... I am using Juzuk's method, I just sum zeros :)

Haskell, 78
print[sum$concat$take x[take x$drop(sum[1..x-1])[1..]|x<-[1,3..]]|x<-[0..100]]
[0,1,16,81,256,625,1296,2401,4096,6561,10000,14641,20736,28561,38416,50625,65536,...

Hope the slightly different output formatting is ok. There's probably a much better way to write this in Haskell, but I felt like solving this in a language I don't often use.

Python 2, 68
Quick and dirty Python solution:
s=0
for n in range(100):s+=sum(range(2*n*n+n+1,2*n*n+3*n+2));print s

source: Stack Exchange

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