text:
Print the alphabet without using each vowel
Inspiration: in 1939, a man named Ernest Vincent Wright wrote a novel called Gadsby without using the letter 'e'.
Your task is to write a set of (up to 5) programs in any language (which has a text-based syntax*) to output all 26 letters of the alphabet in order.  However for each vowel aeiou, at least one of the programs must not include any occurrence of the vowel.
So there must be

a program that does not use 'a' or 'A' anywhere in the syntax of the program.
a program that does not use 'e' or 'E' anywhere in the syntax of the program.
a program that does not use 'i'  or 'I' anywhere in the syntax of the program.
a program that does not use 'o' or 'O' anywhere in the syntax of the program.
a program that does not use 'u' or 'U' anywhere in the syntax of the program.

All of them must output abcdefghijklmnopqrstuvwxyz.
The winner shall be the solution where the length of all programs is the shortest.
* since the constraint wouldn't be much of a challenge in Piet or Whitespace

if one manages to make a single program that does not contain any vowel, do we need multiply the length of the program by 5?

@w0lf No, in that case the length of the single program would suffice.

@w0lf: No, it says "up to 5 programs" and "length of all programs", which I read as "there can be only one program and its length counts in this case".

This doesn't really add much to the existing print-the-alphabet questions.

@PeterTaylor: You don't think having to avoid using vowels in your syntax is a unique challenge?  As a JS programmer, it's especially interesting :)

assembly, anyone?!

Are newlines acceptable in the output (i.e. one per character)? I can shorten some of my code if that is the case...

What if the shebang contain vowels? #/usr/bin/perl -w at least 3 vowels?

@Shamp00 Are we still checking scores? My JavaScript solution beats the crap out of the current one and the JavaScript console one...?

@WallyWest I've updated the scores. (I guess I don't get notified when there's a new answer now that this question has become 'community wiki'...)

damnit; java is ruled out cause even the escape sequence hack doenst work due to requiring a U inside...

@F.Hauri you don't usually count the shebang in code golf anyway, so that's not a problem.

Is uppercase output allowed?

@EriktheGolfer It's not.

@mbomb007 I think it's unclear whether it is allowed or not. OP has specified a string, so my Jelly answer is 7 bytes, not 6. But, if OP allows uppercase, then I will change.

@EriktheGolfer The OP hasn't been on in 2 years. So assume he's not going to get on to allow it. It may be "unclear" to you, but if you look at all the answers, they're all lowercase, so it's just you.

@mbomb007 On profile page: Last seen 2 hours ago. OP is definitely still on PPCG.

I'm the OP. Uppercase not allowed.

Couldn't I just write G in Pyth?

Are functions ok in languages where the main method has to exist and be called main?

I've removed both the automatic leaderboard as well as the (out of dat) list of languages/rankings - it doesn't add anything to the post aside from unnecessary clutter. I've also unprotected the question as I don't see any need for it here

Golfscript - 8 chars
123,97>+

damn, really can't beat golfscript in terms of conciseness...

That being said, the readability stinks like crazy.

It's not that bad ;) generate a list of 123 numbers, remove those who aren't greater than 97, coerce it (array of numbers) to a string.

Use 91,65>+ instead.

Funny to read old comments marveling about how concise Golfscript is now that we have golfing languages like O5AB1E

Brainfuck, 38 chars
++++++[->++++<]>[->+>++++<<]>++[->+.<]

There are, of course, no vowels (or any other letters) in brainfuck syntax.

Valid point there! ;)

30 bytes: ++[[<+++>->++++<]>]<<<<++[->+.<]

PHP, 31 Bytes
No a,e,i,o,u:
<?=~žœ›š™˜—–•”“’‘ŽŒ‹Š‰ˆ‡†…;

The binary string after the tilde has the following hex representation:
\x9e\x9d\x9c\x9b\x9a\x99\x98\x97\x96\x95\x94\x93\x92\x91\x90\x8f\x8e\x8d\x8c\x8b\x8a\x89\x88\x87\x86\x85

Since there's a language scoreboard, I may as well submit this one as well:
Ruby (v1.8) 18 bytes
$><<[*97.chr..'z']

I'm not sure I understand how this works.  Could I get an explanation?

When applied to a string, the ~ operator inverts all of the bits. Here I've inverted abc...xyz. Because there are no symbols characters (or whitespace) in the binary string, quotes are not necessary either.

You may want to specify an encoding for what you have there.

iso-8859-1. Three 'unprintable' characters were removed when it was posted, which is why I included the hex.

Nice and probably the shortest possible PHP version. A command to generate the file: php -r 'echo("<?=~\x9e\x9d\x9c\x9b\x9a\x99\x98\x97\x96\x95\x94\x93\x92\x91\x90\x8f\x8e\x8d\x8c\x8b\x8a\x89\x88\x87\x86\x85;");' > script.php. The command to run it: php -d error_reporting=0 script.php; echo.

Pyth, 1 Character
G

Pyth predefines certain variables. G is predefined as the lowercase alphabet. Pyth also implicitly prints each line with a reasonable return value.

Ninja'd me by 3 years...

Ruby (24 22)
Edit: parentheses can be omitted, 2 chars less:
$><<'%c'*26%[*97..122]

24 chars in Ruby:
$><<('%c'*26)%[*97..122]

How it works
$> is an alias for $stdout or STDOUT. You can write to it using the << operator. The term '%c'*26 repeats the string '%c' 26 times. The % operator is defined on String as an alias to sprintf, so str % val is equivalent to writing sprintf(str,val). The format character %c is used to transform a char value to a char. These values come from [*97..122] which creates an array containing the values from 97 to 122. Et voilá!

Very nice.  I was looking for a way to use << but had forgotten about $>.

I didn't even know about $> before, but i guessed there had to be some dollar-variable alias for $stdout that no one can remember :)

21 characters: $><<[*"`".."z"][1,26] (note: this only works in Ruby 1.8)

@Ventero not only in Ruby 1.8, in Ruby 1.9.2 works as well. But using p [*"".."z"][1,26]` is even shorter.

@Hauleth: No, running it in 1.9 doesn't generate the correct output, as in 1.9 Array#to_s is the same as Array#inspect, whereas in 1.8 it's Array#join - so in 1.9 the output is ["a", "b", "c", "d", "e", ...] instead of abcdef.... For the same reason, p can't be used (it calls inspect on its arguments, instead of to_s).

Awwww, yeah. Now I see that the output was format was given :/ My bad.

J, 26 23 17 16 characters
After an hour or so rummaging around in J's underwear drawer I've finally found a way to eliminate the a. and u: verbs.
2(3!:4)96+#\26$1

Previously:
a.{~96++/\26$1
u:97+i.26

with thanks to randomra for the #\ trick.

Nice solution! Managed to shorten with 1 char using #\  instead of +/\ .

Get out of my underwear drawer

JavaScript (100)
No 'aeou':
this['\x61l\x65rt']('\x61bcd\x65fghijklmn\x6fpqrst\x75vwxyz')

No 'i':
alert('abcdefgh\x69jklmnopqrstuvwxyz')

+1 Nice improvement on my answer :) I had thought about using the \x## codes but weren't sure if they were valid in JavaScript.

why the alerts at all? on a js terminal, objects are echo'd automagically. ('\x61bcd\x65fghijklmn\x6fpqrst\x75vwxyz') @ 42 characters.

@antony.trupe, for code golf, IO is typically done via the language's built in IO mechanisms (or common plugins). For JS this is typically alert, confirm, prompt, console.log, and document.write. Simply declaring a string literal doesn't produce it as output when executed. Otherwise, you'd be correct, and I would have used that.

it produces output(by the definition I use anyways) in the google chrome console, but I concede the issue; it's an arbitrary restriction to begin with.

@antony.trupe, in a language like PHP you'd be able to get away with using a literal, because that's how it performs IO.

K,9
_26#.Q.b6

K,10
"c"$97+!26

K,14
.:".Q.","c"$97

and a silly way to do it with no letters at all (12 chars): (@$`)$97+!26

The K5 way is nearly your second solution but $ takes symbols instead of strings to control the type converted into: `c$97+!26

R, 17 + 19 = 36 characters
no ae (17):
intToUtf8(97:122)

no iou (19):
cat(letters,sep="")

Bash (38)
No vowels at all.
/*/*/*ntf "/*/?ch? {\x61..z}"|/*/b?sh

This program fails on my system, because /*/b?sh does not exist. I have /usr/local/bin/bash, not /bin/bash.

Nice use of shell globbing!

@kernigh [[ ! -d "/bin" ]] && mkdir "/bin"; sudo cp "/usr/local/bin/bash" "/bin/bash"

It would be better if /bin/sh is bash. Then the code can end with /*/sh (36 bytes). But I have not found a system where this works. In Debian, /bin/sh isn't bash. In my old Mac, /bin/sh is bash 2.05b0.(1), but this version is too old and doesn't expand {a..z}.

C, 90 88 84 characters
Compile using gcc -nostartfiles
b;_exit(){for(;b<26;)printf("%c",b+++97);}    // 42 chars, works for a, u
b;_start(){putchar(b+++97)>121?:_start();}    // 42 chars, works for e, i, o

_start and _exit are a nice way to get around main. But if a non-standard compilation line is OK, why not -DX=main?

Somehow, -DX=main feels worse than -nostartfiles does (for me). It is a way to move a part of the source code to the compilation line and it is the same as writing #define X main in the source code which would be clearly invalid. Whereas -nostartfiles isn't a way to rename main, but removes the restriction that there must be a main function (called in _start). On the other hand, using -nostartfiles does feel a bit like cheating, especially as it contains 4 of the 5 "bad" letters :)

It's a slippery slope... The distance from -nostartfiles to -DX=main is small, and then why not save some chars with -DX=main() and so forth. But I can't find a solution that doesn't involve anything fishy.

There's no way you can define the main function to be "mn" for instance?

@Neil, only by doing something like -Dmn=main.  A C function must have a main function unless a non-standard option like -nostartfiles is used.

Golfscript, 10 characters
26,{97+}%+

Why so verbose?

Powershell, 75 62 characters
Edit: Used -f (String.Format) and array indexing to significantly reduce the code length.
'{0}bcd{1}fgh{2}jklmn{3}pqrst{4}vwxyz'-f"$(1|gm)"[8,10,0,5,31]

How it works
gm is an alias for get-members, so 1|gm returns members of the value 1, which is of the System.Int32 type:
PS C:\> 1|gm
   TypeName: System.Int32
Name        MemberType Definition
----        ---------- ----------
CompareTo   Method     int CompareTo(System.Object value), int CompareTo(int value)
Equals      Method     bool Equals(System.Object obj), bool Equals(int obj)
GetHashCode Method     int GetHashCode()
...

"$(1|gm)" returns a string representation of the above list, which happens to contain all the vowels we need to complete the alphabet: "int CompareTo(System.Object value)..."

This isn't stable if MS adds members to System.Int32, though :-)

I think that would have to be ($x=''+$(gv))[8]+"bcd$($x[4])fgh$($x[25])jklmn$($x[26])pqrst$($x[19])vwxyz" which is also 75 characters :)

Argh, right. I fished the wrong item from my history. Sorry.

Actually, if you replace ''+$(gv) with "$(gv)" you get ($x="$(gv)")[8]+"bcd$($x[4])fgh$($x[25])jklmn$($x[26])pqrst$($x[19])vwxyz" which is 74 characters. Nice!

That was probably the one I wanted to get from my history. Although I wrote ''+(gv) I think which has the same length as the inline string expansion (you don't need a subexpression there) :)

I used -f (String.Format) and array indexing to significantly reduce the code length.

BASH: 40 characters

No aeiou used.
No wildcard used.

`tr c-y '\141-w'<<<'rtkpvh %s c'` {b..z}

Ruby, 20 chars
$><<[*97.chr..?z]*''

97.chr is an elaborate way of saying 'a'
.. specifies a Range
?z is a shorter way of saying "z"
the [*range] causes the range to splat al it's values in an array
*'' is the same as join(''); it glues all array values together.
$><< Perlicism: print to stdout.

This code doesn't seem to work. ?z is not shorthand for 'z', but rather for 122. This, however, does work for 18 bytes: $><<[*97.chr..'z']

It does work in Ruby 1.9.

I downloaded 1.9.3... and you're right. Why would they change something like that? I can see why anarchy golf is still running 1.8.7. Anyway, the 18 byte solution works for v1.8.7-

(4 years later...) You can replace 97.chr with ?\x61 for -1 byte.

dc: 18 17 characters
97[dP1+dBD>m]dsmx

And there died a brave character.

I doubt so. I'm wrapping head around it and I don't see any way to shorten it. I have ended with exactly same solution except I used x for register which makes mine solution more obfuscated.

97[dP1+dBD>m]dsmx, 17 characters. Apparently you can always enter hexadecimal characters in DC, but as the input base is ten the value is B*10+D=11*10+13=123='{', and not 0xBD.

Oh, nice glich ;-)

Haskell, 12
['\97'..'z']

Or is this cheating? :)

I admittedly don't know much about Haskell, but it gives me this error: Parse error: naked expression at top level

You run it in the interpreter

MATLAB, 12+20=32 characters
No eiou (12):
char(97:122)

No aeou (20)
fprintf('%s',97:122)

Perl 5, 22 characters
(1) only contains a and e, 10 chars (requires 5.10+, run from the command line):
-Esay+a..z

(2) only contains 'i', 12 chars:
print v97..z

If not allowed to run from the command line, then you need to use use 5.01;say a..z for the first one, at a cost of 7 characters and one more vowel, but it still has no 'i', so it results in a valid entry at 29 total characters.

The '-E' option is ok I think, but usually the 2 characters '-E' are added into the total character length.

@gareth - the -E takes the place of -e for running a one-liner.  If you're running a program from a file, then you're stuck with the use, although you could replace it with the command line option -M5.01 and shave off two more characters.

I was thinking of the rule with the -p option where 2 characters are added to the count. Looking at this meta question though, you should be able to use the -M5.010 for free if that option helps shorten your code.

you could replace your print statement with die to shave off 2 chars

chr 97..z may be replaced with v97..z for 3 bytes.

In Perl,
it's also possible without any vowels
but much harder than in Ruby etc. This uses a total of 101 chars but doesn't require cmd line (perl -e) invocation.
`\160\145\162\154\40\55\145\40\42\160\162\151\156\164\40\123\124\104\105\122\122\40\141\56\56\172\42`

=> Result:
 abcdefghijklmnopqrstuvwxyz
In contrast to the 'similar looking' PHP Solution, this is a real program. The program decoded reads:
perl -e "print STDERR a..z"

After encoding to octal values, another perl interpreter is called during run by the `` (backticks). The backticks would consume the output, therefore it's printed to STDERR.
The encoding is done by sprintf:
my $s = q{perl -e "print STDERR a..z"};
my $cmd = eval(
       '"' . join('', map sprintf("\\%o",ord $_), split //, $s) . '"'
       );

and the eval'd encoding is the program posted (within backticks):
"\160\145\162\154\40\55\145\40\42\160\162"
"\151\156\164\40\123\124\104\105\122\122"
"\40\141\56\56\172\42"

Regards
rbo

You could shorten this to 44 characters by only encoding the vowels :)

APL (Dyalog) (11 13)
You might need an APL font. This is supposed to be Unicode but there's no preview...
Only U (and perhaps ⍳ if counting Greek vowels):
⎕UCS 96+⍳26

(That's: [quad]UCS 96+[iota]26)
Only A:
⎕A

U is a vowel...

@Tobia: and it took over a year for someone to see that (including me). I guess iota is actually also a vowel now that I'm thinking about it. Fixed it.

The APL functional symbol iota (U+2373) is not considered a letter in Unicode, and therefore can't be a vowel.  Note, that it is distinct from the Greek small letter iota (U+03B9).

Python 2, 83
No a, i, o or u; 47:
x=97;s='';exec"s+=chr(x);x+=1;"*26+"pr\x69nt s"

No e; 36:
print"abcd\x65fghijklmnopqrstuvwxyz"

Python 2, 175 characters
Note: prints to output unlike earlier python answer.
Uses 'e', but no a,i,o,u - 63 61 59 65 (fix mistaken i move to lowercase) 115 chars (get rid of spaces).
exec('fr%cm sys %cmp%crt*\nf%cr x %cn r%cnge(97,123):std%c%ct.wr%cte(chr(x)),'%(111,105,111,111,105,97,111,117,105))

(Originally, it used print with a comma that inserted a space; also printed upper case letters.  Now saw stringent requirements for 'abcdefghijklmnopqrstuvwxyz' as output; so adding import statement).
Doesn't use 'e' (uses a,i,o,u; could trivially get rid of a,u for small extension) - 61 60 chars
import string
print string.__dict__['low%crcas%c'%(101,101)]

Your first solution does use the letter i, so it should be: exec('f%cr x %cn r%cnge(65,91):pr%cnt chr(x),'%(111,105,97,105)) and we're back to 64 characters.

exec('fr%cm sys  i mp%crt*\nf%cr...

BioGeek & @Gareth - my manual vowel detection skills suck.  Thanks for point it out; but I had an extra e written as a '%c' so in the end it evens out.

You can remove the parentheses from exec('...')

Ruby, 22
$><<[*?`..?{][1,26]*''

No letters whatsoever :)

Ruby 196 164 44 47
$><<"\x61bcd\x65fgh\x69jklmn\x6Fpqrst\x75vwxyz"

Is this a valid answer, since p outputs quotation marks around the alphabet?

i agree p x is equivalent to calling puts str.inspect, which results in surrounding quotation marks.

@padde you are both right; changed.

@padde I used your $><<, so +1 for that and congratulations; your version is much better

JavaScript (154)
(1) Only contains i (99 chars):
t=this;s=-t+t+t.b;z=s[1]+'bcd'+s[7]+'fghijklmn'+s[4]+'pqrst'+s[21]+'vwxyz';t[s[1]+'l'+s[7]+'rt'](z)

(2) Only contains aeou (55 chars):
t=0;s=''+t.b;alert('abcdefgh'+s[5]+'jklmnopqrstuvwxyz')

Demo: http://jsfiddle.net/SvN5n/

$("h\x65\x61d")[0]["\x6fwn\x65rD\x6fc\x75m\x65nt"]["l\x6fc\x61t\x69\x6fn"]="j\x61v\x61scr\x69pt:\x65v\x61l(`f\x6fr(s='',l=65;l<90;l++){s=s+Str\x69ng.fr\x6fmCh\x61rC\x6fd\x65(l);};c\x6fns\x6fl\x65.l\x6fg(s)`)" 208chars, no aeoui used in code.  Works on chrome browser.

VBA: 76 brute force, 116 without 'cheating' (98 if newlines are acceptable in the output)
Standard Functions
Thanks to VBA's verbosity, I don't believe this can be done without 'E' or 'U' in a standard code module...

"E nd"
"F u nction"
"S u b"

Immediate Functions
Running with mellamokb's assumption, here's without the function declaration (leaving out SUB and FUNCTION) (116 chars, 98 if newlines are acceptable in output):
The below uses neither 'e' nor 'a' (43 chars, formatted to run in the immediate window):
b=65:Do:z=z+Chr(b):b=b+1:Loop Until b=91:?z

The below uses neither 'i' nor 'a' nor 'u' (33 chars, formatted to run in the immediate window):
For b=65 To 90:z=z+Chr(b):Next:?z

The below uses neither 'a' nor 'o' nor 'u' (40 chars, formatted to run in the immediate window):
b=65:While b<91:z=z+Chr(b):b=b+1:Wend:?z

If newline characters are allowed in the output, then the above examples can be shorter:
(37 chars)
b=65:Do:?Chr(b):b=b+1:Loop Until b=91

(27 chars)
For b=65 To 90:?Chr(b):Next

(34 chars)
b=65:While b<91:?Chr(b):b=b+1:Wend

Brute Force
Running with w0lf's Ruby answer
(76 chars, formatted to run in the immediate window):
?Chr(65)&"BCD"&Chr(69)&"FGH"&Chr(73)&"JKLMN"&Chr(79)&"PQRST"&Chr(85)&"VWXYZ"

I think it would be fair to leave Sub..End Sub out, since most other programs don't include function definition.

@mellamokb Well, that makes me feel better. I'll whip up some examples to add to this.

Just think of it as "code you run in the immediate window" :)

Well, if in doubt just call it VBScript which can be included in a file without needing a Sub :)

Fixed a bunch of needless spaces, changed print to ? since that works in the immediate window.

Python 159 117
As mentioned in the other python post the hardest part is dealing with the fact that the only way to output is to use print or sys.stdout.write, both of which contain i. Have to do it with 2 programs (which are freestanding and don't use the python interactive shell to create the output):
This one only uses i for 55 chars:
print"%cbcd%cfghijklmn%cpqrst%cvwxyz"%(97,101,111,117)

This one avoids using i for 104 chars:
eval("sys.stdout.wr%cte"%105,{'sys':eval("__%cmport__('sys')"%105)})("%c"*26%tuple(range(97,123))+"\n")

EDIT:
Massive breakthrough!!! I was thinking that use of eval (or even exec) was a bit of a cheat and not truly in the spirit of the competition. Anyway, trawling through the builtins I found a way to get hold of the print function without using i. So here is the avoid-i (and o) program for 68 chars:
vars(vars().values()[0])['pr%cnt'%105]("%c"*26%tuple(range(97,123)))

But because that also avoids o, this can be paired with one that only avoids a, e, u for 49 chars:
print"%cbcd%cfghijklmnopqrst%cvwxyz"%(97,101,117)

You can toss away compatibility, and gain a character - vars(vars().values()[0]).values()[47]

Rebmu: 15 characters
Ctc'`L26[pn++C]

Reading Rebmu always requires a bit of unmushing to start with:
c: tc '` l 26 [pn ++ c]

Then it helps to expand the abbreviations:
c: to-char-mu '`
loop 26 [
    prin ++ c
]

It would be more obvious using a character literal for the predecessor of lowercase a:
c: #"`"
loop 26 [
    prin ++ c
]

But that doesn't "mush", so converting a word literal to a character passes for the same purpose.  What I like about it, as with most Rebmu, is that it has the spirit of a sensible program despite the compression.  (The Golfscript answer is shorter but doesn't map to the way a programmer would usually think when coding.)

<>< (Fish) - 22 characters
Because <>< uses the 'o' to print a character, this challenge seems impossible to do. Luckily, fish can change its own code in runtime. This allowed me to add the print instruction to the code.
This code uses none of the vowels:
'`78'+11pv
:X:'z'=?;>1+

You can run the code here

Ruby, 47 characters
(1) Only contains 'a' and 'u', 24 chars:
puts [*97..122].pack'c*'

(2) Only contains 'o' and 'i', 23 chars:
$><<[*97.chr..'z'].join

There's a slight difference in output in that the first one adds a newline and the second doesn't.  Could add the newline to the second at a cost of 4 characters; removing it from the first would be harder.

PHP, HTML (50)
No 'aeiou':
abcdefghijklmnopqrstuvwxyz

abcdefghijklmnopqrstuvwxyz

I only see HTML.

@joar, if you place the same text in files named index.html and index.php, you would get the same output.

@zzzzBox I know that, because PHP only processes code within <?php (and <?, <?= if you have short tags enabled) blocks. Still, this is not a PHP example since it does not contain any valid PHP code or even a PHP code block. It's HTML with character entities.

@joar, PHP will output any code within the file that is not within <?php ?> tags, because it is designed as a templating language for HTML, which makes this genuinely PHP code, I'm simply not using any of the dynamic features of the language.

@zzzzBox well, let me port your username to PHP: zzzzBox Released under the MIT license.

@joar, I can't tell if you're trying to be humorous, it seems to have been lost on me.

It was a humouros comment. My point is that you may pipe anything through the PHP interpreter as long as it doesn't contain any PHP blocks, Doing that does not magically turn it into PHP code.

@joar, it's not magic, but it is valid PHP. You can't pipe anything through the PHP interpreter, you need to pipe valid characters in the correct encoding. HTML happens to be valid PHP because it's used as a subset of the language.

wouldn't PHP be the subset of HTML? As you said, [OHP]  is designed as a templating language for HTML -- My point is that PHP does not parse HTML, leaves it as it is, it does not even validate it -- You may pipe Hamlet through PHP but that does not mean you've written hamlet in PHP -- Your implementation is written in HTML and the only thing you can do to make even half-PHP is to wrap it in  <?='...'?>.

Nope, HTML is a subset of PHP, PHP includes everything that HTML can do, in addition to other capabilities. PHP has to parse the entire contents of the page to find the <? tags, so the HTML is parsed, and then passed through. Hamlet can be piped through PHP in the same way that you can pipe Hamlet through an HTML file and have it be HTML. Comments are not the appropriate location for these extended discussions, so send me an email if you wish to resolve your confusion.

PHP does not parse the HTML, it scans it for the next PHP block start tag. see the definitions of parse.

PHP does indeed output the text.  The problem is, this PHP program doesn't output the whole alphabet.  It outputs some of the letters, along with various other characters like #.  The entity decoding is done by HTML.  You could use html_entity_decode to get around this (of course it has 3 vowels, so you'd need to deal with that).

Postscript, 46 45
(\141bcd\145fgh\151jklmn\157pqrst\165vwxyz)=

You can shorten that by one character by removing the space.

Scala,38+17=55
No 'aeio':
'\u0061't\u006f'z'm\u0061p pr\u0069nt

No 'u':
'a'to'z'map print

Output: abcdefghijklmnopqrstuvwxyz

Your answer only satisfies 'e' and 'u'.  You need to add a version that does not use 'a', 'i' and 'o'.

@shamp00: +1 Now fixed

You still need the no 'u' version too.  The task is to have as many programs as necessary to cover all 5 vowels.  Then you add the lengths together for the total score.

Regarding what @shamp00 says, just add back in your ('b'-1).toChar to'z'map print and you're good to go!

@Gaffi: ok. let me add my original version.

JavaScript (single program, no vowels whatsoever) 104 99 92 90
Edit 1: []["s\157rt"]["c\157nstr\165ct\157r"]('\141l\145rt("\141bcd\145fgh\151jklmn\157pqrst\165vwxyz")')()
Edit 2: 3[$="c\157nstr\165ct\157r"][$]('\141l\145rt("\141bcd\145fgh\151jklmn\157pqrst\165vwxyz")')()
3[$="c\157nstr\165ct\157r"][$]('\141l\145rt`\141bcd\145fgh\151jklmn\157pqrst\165vwxyz`')()

Edit 1: Previously used "filter" as my array trigger to access global object, reduced it to "sort" for a saving of 5 chars.
Edit 2: Reduced initial array to 3 to obtain constructor primitive and reused constructor recursively to shave off 7 chars, many thanks to @Firefly for the inspiration.
Edit 3: Reduced (" and )" in single-quoted string to backticks, shaving a further 2 characters.

Brainfuck, 25 bytes
One byte improvement c/o Sp3000.
+[+<+<+[>]<-<+<+]>[+>+.<]

Try it online!
The initial bit +[+<+<+[>]<-<+<+] initializes the tape to:
[0, 106, 106, 0, 230, 96, 0, 135, 0]
              ^

This is an ideal tape (as 230 is 256-26).

26 bytes
--[->-[<]>+>-]>[+++<<+.>>]

Try it online!
Exactly one byte per letter. The initial bit --[->-[<]>+>-] initializes the tape to:
[0, 0, 0, 0, 0, 96, 0, 178, 0]
                    ^

178 is conveniently 256 - 26·3.
Alternatives
-[-[+>--<<<]>>>]>[->-.++<]
+[+[->++<<]>>+>+]<+[-<+.>]

25: +[+<+<+[>]<-<+<+]>[+>+.<]

My pruning logic seems off - it was detected as an infinite loop. I may need to re-crunch some results >.<

Java (OpenJDK 8), 137 bytes
$->""+($=97)+ ++$+ ++$+ ++$+ ++$+ ++$+ ++$+ ++$+ ++$+ ++$+ ++$+ ++$+ ++$+ ++$+ ++$+ ++$+ ++$+ ++$+ ++$+ ++$+ ++$+ ++$+ ++$+ ++$+ ++$+ ++$

Try it online!
Similar to another answer of mine in Java. (Ab-)uses the lack of a "no input" rule.

Brilliant! Upvoted both your answers. Very original, especially for a Java answer.

@KevinCruijssen Thank you! I've had a hard time making the first one (the other one), but this one was very, very similar.

C, 136 115 104 characteres
A C program must have a main function. So my code is valid, except for these a and i.
Prints a newline at the end. Can save some characters by removing it.
No e,i,o, 50 chars:
f(x){putchar(x?123-x:10),x--&&f(x);}
main(){f(0);}

No a,u, 54 chars:
f(x){printf("%c",x?123-x:10),x--&&f(x);}
main(){f(26);}

"A C program must have a main function" - This SO question taught me this isn't true, see my answer :)

@schnaader, the ANSI C standard says "The function called at program startup is named main". Your code does work, but I'm not sure how portable it is (not that the question requires portability). Anyway, I'll stick to main.

Python shell, 94 78 chars
It prints the alphabet when running in an interactive shell (which prints the expression it evaluates).
Python isn't the tool for this task. Printing requires print, loop constructs require in or while, so i is quite a problem.
Both these expressions evaluate to the a-z string. The first doesn't use i,o, the second doesn't use a,e,u
"%c"*26%tuple(range(97,123))
''.join([chr(ord(c)-1)+c for c in'bdfhjlnprtvxz'])

Brute-force approach, 110 chars:
"%c"*26%(97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122)

eval's got no i.

@boothby Yes it does: evil. There.

Languages are defined by their implementation. A Python shell is not a normal implementation of Python, so it's a "different language". http://meta.codegolf.stackexchange.com/a/7844/34718

Javascript (139 chars), logging to console:
Uses no 'aeou' (95 chars):
q=''+{};w=q[1];this['c'+w+'ns'+w+'l'+q[4]]['l'+w+'g']('\x61bcd\x65fghijklmn\x6fpqrst\x75vwxyz')

Uses no 'i' (44 chars):
console.log('abcdefgh\x69jklmnopqrstuvwxyz')

I count here 95 and 79 characters, respectively.

@Gaffi Thanks haha. I wrapped it in double quotes and used .length to get the length. Of course the \x75 and such were counting as one character haha, oops.

It happens. :-)

PHP, 47
All credits to mellamokb
<?="\x61bcd\x65fgh\x69jklmn\x6fpqrst\x75vwxyz";

You can shorten by using string concatenation instead of exiting tags: <?=chr(97).'bcd'.chr(101)....  Also, you can make even shorter by using the hex escape sequences <?="\x61bcd\x65...".  Here's some examples of alternative shorter solutions, the last is the shortest at 47 characters (note also that you can safely leave the final closing tag off to save 2 chars): http://ideone.com/7aAQh

Factor, 264 characters
No ae, 60 characters:
USING: io ;
"\u000061bcd\u000065fghijklmnopqrstuvwxyz" print

No io, 102 characters:
USE: eval
"USE: \u000069\u00006f
\"abcdefgh\u000069jklmn\u00006fpqrstuvwxyz\" pr\u000069nt" eval( -- )

No u, 102 characters:
FROM: math.ranges => [a,b] ;
FROM: io => print ;
FROM: strings => >string ;
97 122 [a,b] >string print

Every language, in the previous answers, uses less than 200 characters. Factor is the only language to use more than 200 characters and to use 3 programs. Factor is difficult, because outputting without io is a challenge, and programming without u is almost impossible.
The first 2 programs are variations of
USE: io
"abcdefghijklmnopqrstuvwxyz" print

Alternatives to io are scarce; formatting still needs i and o, and prettyprint needs i. I saw string evaluation in a Python answer, and took the hint. With eval, I can escape away i and o, but I need a and e in eval, and u in \uxxxxxx escapes.
The hardest challenge is to remove u. This means no USE:, USING:, \uxxxxxx, nor sequences. My best program without u needs all of aeio. I would like a Factor program without aeu, but my only way to remove ae is to use u.

Sorry, wasn't thinking straight! RENAME: each-integer math => # 26 [ 65 + write1 ] #

Perl 5.10+, 8 + 22 = 30 chars
No e, i, o, u:
say a..z

No a, i, o, u:
s//"s\x61y \x61..z"/ee

Both of these need the -M5.010 switch (which is considered free) to enable the say feature.  For older perls, it can be replaced with print for an extra four chars (and loss of trailing newline in output):
print a..z
s//"pr\x69nt \x61..z"/ee

Bash 34 characters
This is my 34 characters long bash snippet, close to marinus snippet but shorter :
/*/?ch? $'\145ch\157 {\x61..z}'|sh

Perl (25 24 ) (18?) (no wowels, little cheating)
script.pl contains:
$"="";s//@{["\x61"..z]}/

it has to be executed this way:
echo | perl -p script.pl

or
echo | perl -pe '$"="";s//@{["\x61"..z]}/'

If you don't mind spaces between letters in the alphabet, it can be shortened to 18 characters:
s//@{["\x61"..z]}/

($" variable defines separator to be used for printing arrays, space is default)
UPDATES:

s/^/ -> s//

You could whipe (useless) pipes! perl -pe 's//@{["\x61"..z]}/' <<<''

Tcl, 49 chars
p\165ts \141bcd\145fgh\151jklmn\157pqrst\165vwxyz

Yeah, \ substitution works for commands. (And all other kinds of substitution as well)

demo

The shortest iterative algorithm I can devise is longer, even before applying the no vowels restriction, having 51 bytes: while {[incr n]<27} {puts [format %c [expr $n+96]]}

Shorter without restriction is 45:time {puts [format %c [expr [incr i]+96]]} 26

Javascript, 96
No "aeiu"
throw('\x61bcd\x65fgh\x69jklmnopqrst\x75vwxyz')

No "o"
eval("thr\x6fw('abcdefghijklmn\x6fpqrstuvwxyz')")

Run it from console
Chrome

Firefox

How do I run this? I can't get it to work with JSFiddle, nor in onload().

@shamp00 You can run it from you browsers console, i edited the answer and added 2 screenshots =)

Matlab: 11 characters
['' 97:122]
% Or equivalently
['' 97]:'z'

If it is allowed to output more than just the alphabet, this can be reduced to just 7:
'`':'z'

Very nice! Contatenating '' to convert to string

Fission, 21 bytes
~MR' @'`~~~~~~
S[+!
*

Control flow starts at R with a right-going atom. First we set the mass to 32 with '<space>. @ swaps mass and energy. '` sets the mass to 96, so our atom is now (96,32). We decrement the energy seven times with ~ to get (96,25) (note that the code is toroidal). M redirects the atom downwards and [ to the right. We're now on the second line. + increments the mass, the ! prints the corresponding character. By doing this repeatedly we print the alphabet starting at a. As long as the energy is still positive, the S will let the atom pass straight through, such that we keep looping through the second line. However, while doing so it will also decrement the energy. Once the energy is 0 (and we've printed z), S will instead deflect the atom downwards, where it hits *, which terminates the program.

Cardinal, 22 20 chars
%n->,#~n'!@
 b ^+< y

output:
Executing program..

abcdefghijklmnopqrstuvwxyz

Execution complete.
>

Mathematica, 61 bytes
Yeah, total thread necro. Just wanted to see if I could do it at all! (Mathematica command names tend to be pretty verbose and thus vowel-heavy....)
Each of the two commands
Alphabet[]

and
Union@@(StringSplit[#,""]&/@WordList[][[443;;692]])

outputs a list of the 26 lowercase letters in order. StringSplit[#,""]& splits its input string at every occurrence of "", that is, between every character (hence accomplishes the same as the command Characters@#, but without that nasty "a" or "e"). This is applied to a set of 250 words, namely the 443rd to 692th words of the built-in word list. (The 443rd word, "adequateness", is needed for its "q", while the 692nd word, "aftershock", is needed for its "k". None of the first 427 words contains an "x", and the 428th word, "add-on", has an unfortunate hyphen; so we had to start over to find a contiguous block that works.) Finally, Union removes repetitions and sorts the list to boot.

JavaScript (Node.js), 32113 bytes
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Try it online!

Perl 5 -p, 21 bytes
}{$\.=$_ for"\141".._

Try it online!

Japt, 2 bytes
;C

Test it here

We can now use languages made after the question was posted, right?
Charcoal, 1 byte
β

Try it online!
In Charcoal, β is a predefined variable containing the lowercase alphabet, so no vowels there.

this works now too :P (verbose mode)

JS (ES2018), 54 bytes
\141l\145rt`\141bcd\145fgh\151jklmn\157pqrst\165vwxyz`

Alerts "abcdefghijklmnopqrstuvwxyz".
So, you can update the JS score to 54 bytes.

D no 'u' (64 chars)
import std.stdio;void main(){for(char c=96;c++<'z';){write(c);}}

D only i (92 chars)
mixin("imp\157rt std.stdi\157;v\157id m\141in(){f\157r(ch\141r c;c++<'z';){writ\145(c);}}");

abusing the mixin and octal escape in string literals

What about the complementary program(s) that don't use a,e,i,o?

@mellamokb check now :)

You still need a version with no i.

BASH: 16 + 32 = 48 characters
Here's some inspiration to all you shell-lovers:
Using a, i (no e, o, u): 16 characters
printf %q {a..z}

Using e, o (no a, i, u): 32 characters
$0<<<$'echo {\x61..z}|tr -d " "'

works well, providing you've set your computer up with an automatic
#!bin/bash

I'm sure someone out there knows how to un-vowel this!

Burlesque, 12 characters
'`'zr@[-\[sh
(see here in action.)
With a: 'a'zr@\[sh

C# – 278/149
Variant 1 – Full standalone programs
A and I are unavoidable here because of class and static.
Without U: 81 chars:
class C{static void Main(){for(int x=65;x<91;++x)System.Console.Write((char)x);}}

Without E: 96 chars:
class C{static void Main(){for(int x=65;x<91;++x)Syst\u0065m.Consol\u0065.Writ\u0065((char)x);}}

Without O: 101 chars:
class C{static int Main(){System.C\u006fns\u006fle.Write("abcdefghijklmn\x6fpqrstuvwxyz");return 0;}}

Total (with A, I missing): 278
Variant 2 – Pure code
Without A, E, I, O: 97 chars
Syst\u0065m.C\u006fns\u006fl\u0065.Wr\u0069t\u0065("\u0061bcd\u0065fgh\x69jklmn\x6fpqrstuvwxyz");

Without U: 52 chars
for(int x=65;x<91;++x)System.Console.Write((char)x);

total: 149

class C{static void Main(){for(var x='@';x++<'Z';)System.Console.Write(x);}} shorter one for first program.

 Befunge, 26
>"`">1+:"z"`v
:,  ^      @_

Minimizing whitespace is part of the challenge of Befunge, so I included it in the character count. It might be possible to take out some of that whitespace, but the instructions themselves seem minimal.

You can save quite a few characters. The first > is unneeded and you can arrange on lines. Also, Befunge 98 has ', the fetch character. I suggest doing this: 1st line: 'backtickv, second line: :,>1+:'zbacktick!j@ for a total count of 16 chars.

Smalltalk (Squeak 4.x) 78 chars
Since we program by sending messages to objects, and that most messages are made of english words, this is a real challenge in Smalltalk.
However it is possible to exploit this curiosity: we can concatenate a String and a ByteArray with binary selector ,
'',#[97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122]

We can also exploit arithmetic on ByteArray to shorten to 78 chars
'',(#[0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25]+97)

Now can we write a loop without using to:do: whileTrue: repeat?
Yes we can, with recursion, but we need to stop the recursion with a test, and can we without using one of ifTrue: ifFalse: or: and:?
Yes we can just implement the message of our choice in True/False.
Let's see how far we can go...
We can't use the receiver of a message, self has a vowel: so we need a message with two parameters, say x:z:, sent to any object (9 chars)
0x:''z:97

we implement x:z: message in Object (38 chars - 47 total)
x:x z:z z<123?[^0x:x,(#[0]+z)z:z+1].^x

we implement ? in class False (2 chars - 49 total):
?x

we implement ? in class True: (6 chars - 55 total)
?x^x x

But now, how to evauate the block without sending the message value (3 vowels)...
The best I could was to implement x in class BlockClosure: (16 chars - 71 total)
x<primitive:201>

But that still consumes 2 vowels... And we're not far from original 78...
I still got a nice obfuscation - golfing in Smalltalk is really contre-nature ;)

Sage CLI, 42
No e,i,o,u:
map(chr,[97..122])

No a,i,o:
'%c'*26%tuple([97..122])

Fun fact: str, chr, and cmp are the only Python builtins that don't contain vowels!

Brainfuck, 31 bytes
-[----->++>+<<]>----->+[--<.+>]

How it works
-              wrap to 255
[----->++>+<<] loop 51 times  r1=102 r2=51
>----->+       r1=97 r2=52
[--<.+>]       loop 26 times and print letters a-z

I was wondering when a Brainfuck solution would rear its head... +1

Perl 5.10+, 23 chars
(This is an improvement on previous such entry but I don't have the reputaion to comment there):
no a, e, o, u:
print "\x61"..z

no e, i, o, u:
say a..z

Marbelous, 94 Bytes(I think)
.. @1 61 ..
.. .. // ..
.. Dn \\ ..
++ =0 \/ ..
@1 !! .. ..

:Dn
}0 .. 85 }0 }0
\\ {0 // {> {<

One program, no vowels, I think this qualifies as text-based, but I could be wrong. Marbelous interpreter

I think this is 94 bytes (unless there was whitespace originally that wasn't put into your answer).

Piet, 104 (8x13) codels
Not eligible for this challenge, but I did it nonetheless.

I guess I could golf it a bit more, but this should be a good start.
output:
D:\codegolf\npiet-1.3a-win32>npiet "alphabet codegolf.png"
abcdefghijklmnopqrstuvwxyz

Not eligible to win as the question says “any language (which has a text-based syntax*)”, but nice one anyway.

I know. I did it just for the fun of it and wasn’t going for winning the challenge. :)

05AB1E, 4 bytes
žpRl

Try it online!
Doesn't use any vowel. If it were to use vowels, It'd be just this instead.
A

Kotlin, 112 111 bytes
No E O U (29 bytes)
{('A'..'Z').map{println(it)}}

No A (39 bytes)
{(('B'-1)..'Z').filter{print(it);2>=1}}

No I (44 bytes)
{('A'..'Z').map{z->System.out.format(""+z)}}

Pyth - 1 Byte
G

Implicitly print alphabet

Implicitly Print Alphabet. IPA.

Keg, 8 bytes (SBCS)
b;(|:1+

TIO

Keg, 7 bytes (SBCS)
\`zɧ^_^

This generates the range from backtick to z and removes the backtick character.

W, 8 bytes
97;122.C

Pretty simple:
97;122.  % Generate a range from 97 ('a') to 122 ('z')
       C % Convert this to its character form

Keg, 4 bytes
b;zɧ

Generates a range from a to z and prints it.
Try it online!

W d, 5 4 bytes
(ÇL·

Explanation
After decompression:
'a    % Character a
  'z. % Up to character z

Vyxal, 3 bytes
kB∷

Try it Online!
Explanation:
kB   # Built-in constant "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz"
  ∷  # Second half of the string
     # Implicit output

Alternate 3 byte solution
kzṘ

Try it Online!
Explanation:
kz   # Built-in constant "zyxwvutsrqponmlkjihgfedcba"
  Ṙ  # Reverse the string
     # Implicit output

Vyxal, 3 bytes
kzṘ

Try it Online!
I cannot get more shorter than that. Sadly Vyxal is unable to beat Pyth here.
Fix thanks to @AUsername

Read the challenge. One mustn't have a in it. kzṘ works tho

C 108
Technically cheating, but
x[]={1684234849,1751606885,1818978921,1886350957,1953722993,2021095029,31353};y(){z("%s",x);}

Compile with -Dy=main -Dz=printf (I counted those towards the char count).
Of course if you're allowing -D, go full hog and say
-Dp=main(c){for(;c<27;)putchar(96+c++);}
39 characters there. (Or one, depending on how you count).

With the same method, you could shorten a lot with "abcd%cfg....

Yes, but the the array was more intimidating. That's half comprehensible.

Lua, 56
_G["pr\105nt"]"\97bcd\101fgh\105jklmn\111pqrst\117vwxyz"

Erlang escript 75
It's pretty hard to do any golfing in Erlang but anyway:
$ cat alphabet

'm\x61\x69n'(_)->
'\x69\x6f':'f\x6frm\x61t'('l\x69sts':'s\x65q'(97,122)).

Note empty line at beginning of escript and also line break in main function. They are both mandatory. Run it using
$ escript alphabet

MATLAB, 17 characters
x='`':'z';x(2:27)

NOTE: Would be a winner with 7 characters if the first letter wasn't a vowel :-)
'a':'z'

F# (96) characters, using fsharpi
// Without u (48 chars)
sprintf "abcdefghijklmnopqrst%cvwxyz" (char 117)

// Without a, e, i, o (48 chars)
"\u0061bcd\u0065fgh\u0069jklmn\u006fpqrstuvwxyz"

This was tough since all the functions to manipulate sequences contain vowels.  Also the functions for outputting to stdout are printf and printfn, therefore this only produces a string instead of writing it out.
These lines will need to be ran through the F# interpreter and ended with ;; to execute.

Python shell, 48 + enter
str('\x61bcd\x65fgh\x69jklmn\x6fpqrst\x75vwxyz')

Output:
'abcdefghijklmnppqrstuvwxyz'

If this is valid, I think my answer is too?

Powershell, 29 + 39 = 68 chars
If newlines are acceptable in the output (as has been asked in the question's comments), this can be further reduced to 51 chars.
Uses no 'eiou' (29 chars):
$s="";$s+=97..122|%{[char]$_}

Uses no 'au' (39 chars):
-join(97..122|%{new-object string($_)})

Both work off of the same concept of translating integers into their ASCII values, the first by an explicit cast to char and the second by using the string constructor to perform the cast implicitly.

The "no eiou" solution doesn't output anything, and the variable has a bunch of spaces in it which weren't in the question spec. (Though, having not yet gotten an answer for newlines, I'm not sure we can assume any whitespace is out.) You'd need to add ;$s (3 characters) to make it output.

That said, you could stick with the same principle and even shorten it by 3. 97..122|%{$s+=[char]$_};$s This also eliminates the spaces.

Another variant of the 39-character script. Same length. 97..122|%{$s+=new-object string($_)};$s

another modification to the first one which eliminate spaces $ofs='';"$(97..122|%{[char]$_})" however it adds an 'o' and is now 32 characters.

Forth, 46
.\" \x61bcd\x65fgh\x69jklmn\x6fpqrst\x75vwxyz"

C (77)
Here's my crack at it. Dunno if I broke some kind of anti-compiler-flag rule, but here goes:
int main(){int i=97;while(++i<'{')if(i^'e'&&i^'i'&&i^'o'&&i^'u')putchar(i);

To compile and run:
$ gcc az.c -include "stdio.h" -o az
$ ./az
bcdfghjklmnpqrstvwxyz

In case anyone's interested, here's a quick explanation of some of the 'micro-optimizations':
97 is the decimal equivalent of 0x61, or 'a'. Used because it saves one char over 'a'.
'{' is the char immediately after 'z', it saves me an = (i<='z' vs i<'{').
A^B returns 0 when A and B are equal, and anything but when they aren't, which is as good as != for my purposes. It saves me four chars.
Loop starts out immediately ++'ing i to skip 'a' from the get-go, and save me an extra two chars. It saves me 9 chars altogether (exclude i^'a'&& and the i and ; I would've had to put had I incremented i within the block)
And finally, I used a compiler flag to include stdio.h instead of putting it in the file, saving me 18 chars. I don't know if this is "cheating" or anything, so feel free to point it out if it is.
P.S. This is my first code golf, so if I'm missing a rule, spoken or not, don't hesitate to correct me.

This program uses the letters a and i (in main) and e, o, and u in if(i^'e'&&i^'i'&&i^'o'&&i^'u'). I suspect you've misunderstood the question.

@Gareth I probably did. I interpreted the goal as to "make a program that prints every letter in the alphabet (sans a,e,i,o,u) in the shortest amount of code you can manage."

@Gareth Oh. Yes, I completely misunderstood the question. I thought the output was supposed to exclude vowels, but the source was fine including them. It was the other way around.

Bash, 31 chars
I think this is the shortest bash version so far:
z=({Z..z});tr -d \ <<<${z[@]:7}

This one outputs exactly abcdefghijklmnopqrstuvwxyz with no whitespace between any letters.

Clojure: 81 over 2 statements
No i, o, or u: 35 chars
(apply str(map char(range 97 123)))

No a or e: 46 chars
(str \u0061"bcd"\u0065"fghijklmnopqrstuvwxyz")

REPL (RPL?) session:
cd-glf-s-hrd> (apply str(map char(range 97 123)))
"abcdefghijklmnopqrstuvwxyz"
cd-glf-s-hrd> (str \u0061"bcd"\u0065"fghijklmnopqrstuvwxyz")
"abcdefghijklmnopqrstuvwxyz"

Cjam 6
'{,97>

creates the character "{"
lists all characters less than "{" (this ends if you try to print it because character 0 stops things from outputting)
removes any with a value less than or equal to 97

CJam was created after this challenge was posted.

@ThomasKwa I realised that after having answered it. This disqualifies it from winning, but I think it is interesting enough it shouldn't be removed.

Haskell (interpreted), 17
[['`'..]!!1..'z']

Back-quote comes before 'a', so a is the second element of the sequence starting with back-quote. This is then just the sequence from a to z.
This is technically a naked Haskell expression. (If you save it to ".ghci", though, running ghci will print the alphabet.)

T-SQL, 120 (65+55)
This answer assumes results of both PRINT and SELECT are allowed as output.
65 characters without e, o, u:
PRINT'abcd'+CHAR(101)+'fghijklmn'+RTRIM(0x6F707172737475)+'vwxyz'

55 characters without a, i:
SELECT LEFT(0x616263646566676869,9)+'jklmnopqrstuvwxyz'

><>, 35 bytes
!v99*:f1++$ff++31p!
 >: 1+:bb*1+)?;

><> outputs with the command 'o', hopefully it also provides introspection capability so we'll just edit the code at runtime to add the 'o'. This is done with the command 'p' at the end of the first line.

Simplex v.0.7, 3 bytes
^lg
^l  ~~ sets current byte to the alphabet [a-z]
  g ~~ output as string

Groovy, 15 + 10 = 25 bytes
{'\u0061'..'z'}

Defines an anonymous function that returns the alphabet. Does not use a, e, i or o.
{'a'..'z'}

Defines an anonymous function that returns the alphabet. Does not use e, i, o or u.

Jelly, 7 chars
”Ø;97ỌV

Try it online!
Seems like this should (not (non-competing)) be accepted instead of GolfScript.
Note:
Ø and Ọ are not O, so this is valid. Here is how I built it:
My initial program (2 bytes) was:
Øa

But, since it contained an a, I had to change it.
This could have been a valid 6-char program if uppercase output was allowed:
65r90Ọ

The language is way newer than the challenge, so no, it should not be accepted instead of Golfscript. See this meta

@sanchises Oh, if it is newer, then OK. I thought it was appropriate, since I neither knew when the first commit was made nor when the required commit for this to work was made.

I guess the purpose of that rule is also to prevent flooding of old challenges with new languages - golfing languages are now much more commonplace.

@sanchises I don't think it's there for that reason; it's there to prevent cheating by creating languages which just do the task on encountering the empty program.

Note: "I guess (...) also (...)". I know what the main reason is for the rule, but it's strictness has some side effects that I'm sure were considered, and not seen as a deal-breaker for making the rule so strict, which generally means the side-effects were considered at least somewhat beneficent. But that's just my interpretation of ppcg politics. ;)

Python 2, 91 bytes
Vowels are escaped with octal where necessary.
No ae
print"\141bcd\145fghijklmnopqrstuvwxyz"

No iou
exec"pr\151nt''.j\157\151n(map(chr,range(97,123)))"

Java 8, 517 262 characters
-255 bytes thanks to @OlivierGrégoire.
No aeio (165):
\u0069nt\u0065rf\u0061c\u0065 M{st\u0061t\u0069c v\u006F\u0069d m\u0061\u0069n(Str\u0069ng[]b){f\u006Fr(ch\u0061r c=97;c<123;)Syst\u0065m.\u006Fut.pr\u0069nt(c++);}}

Try it online.
No u (97):
interface A{static void main(String[]a){for(char c=97;c<123;)System.console().printf("%c",c++);}}

Note that the program for u makes use of System.console(), which will return null (and thus cause the code to throw a NullPointerException) if you call it from anything other than your OS' native terminal (cmd on Windows, bash on Linux/OSX, etc.)

You can use System.err.printf("%c",c++); for u source code in place ofSystem.console().printf("%c",c++);

You should mash them all in 2 programs: one without a, e, i, o and another without u.

05AB1E, 4 bytes
žpRl

Try it online!
Explanation:
žp     Push 'ZYXWVUTSRQPONMLKJIHGFEDCBA'
  R    Reverse string - 'ABCDEFGHIJKLMNOPQRSTUVWXYZ'
   l   Lowercase - 'abcdefghijklmnopqrstuvwxyz'
       Implicitly print

Perl 6, 49 bytes
("a".."z").map(*.print) # 23 bytes, no E, O, or U
$*OUT.put((97..122)>>.chr) # 26 bytes, no A, E, or I

Befunge-98, 19
'`1+>:#;,1+:'{-#;_@

Explanation:
'`1+                   Initialize stack with ascii value for 'a'
     :  ,              Duplicate top of stack, print it
         1+:'{-        Increment top of stack, push zero if ascii value after 'z'
    > #;       #;_@    Loop until top of stack is zero, then end

V, 5 bytes
¬`{Ó×

Try it online!
Explanation
¬`{                         " inserts characters in range `to {

This outputs
`abcdefghijklmnopqrstuvwxyz{

To remove the extraneous output, we can use a replacement
Ó×                          " remove every non-alphanumeric character in this line

                            " synonym of vim's :s/\W//g

Alternatives
¬`z|x                       " prints every character from ` to z and
                            " removes the first character

Bean, 38 bytes
Hexdump:
00000000 37 cd a0 5e 80 25 81 00 cc a0 5e 84 25 81 01 80  7Í ^.%..Ì ^.%...
00000010 26 4d a0 5d 81 53 d0 80 a0 0e 20 80 24 4b 80 20  &M ].SÐ. . .$K.
00000020 5e b9 37 b1 b2 33                                ^¹7±²3
00000026

The equivalent JavaScript is:
for(b=97;b<123;)a+=String.fromCharCode(b++);

Alternatively, another 38 byte solution is:
00000000 bc 81 3d a0 5e 25 81 00 35 cc a0 5e 84 25 81 01  ¼.= ^%..5Ì ^.%..
00000010 26 4d a0 5d 81 53 d0 80 a0 0e 20 80 24 4b 80 20  &M ].SÐ. . .$K.
00000020 5e b9 37 b1 b2 33                                ^¹7±²3
00000026

which is equivalent to the JavaScript:
var b=97;while(b<123)a+=String.fromCharCode(b++);

This takes advantage of the fact that a is defined as "" when there is no input, and that the last executed a+=... is implicitly printed, and contains the full string of the alphabet.

Befunge, 16 bytes
1+:"`"+,:55*`#@_

Try it online!
Explanation
1+                  Increment the loop index which start with an implicit zero.
  :"`"+             Make a duplicate and add 96 to convert that into a lowercase letter.
       ,            Write the letter to stdout.
        :55*`       Check if the index is greater than 25 (i.e. it's the last letter).
             #@_    If so, branch left and exit, otherwise branch right and loop.

DUP, 16 bytes
97[$123<][$,1+]#

Explanation:
97                  {push ASCII for “a” on stack}
  [     ][    ]#    {while [this is not 0][do this]}
   $                {duplicate top stack element}
    123             {push 123 on stack (ASCII value of “z”+1}
       <            {2nd element < top element? if true then push -1, if false then push 0}
          $         {duplicate top stack element}
           ,        {print character of top stack element to STDOUT}
            1+      {add 1 to top stack element}

Online DUP interpreter is available here.

Recursiva, 1 byte
)

Try it online!

Why would this be non-competing?

@LyricLy Because The feature(in fact the whole language) was made later to the problem? :D I am unsure though!

We have consensus that newer languages are no longer non-competing.

VBA, 70 Bytes
Unfortunately having one brute force solution was better than having multiple looping solutions :(
Anonymous VBE immediate window function that takes no input and outputs the capitalized alphabet to the VBE immediate window
?Chr(97)"bcd"Chr(101)"fgh"Chr(105)"jklmn"Chr(111)"pqrst"Chr(117)"vwxyz

Sinclair ZX80 BASIC, ~26 [tonkenized] BASIC bytes
 1 FOR O=38 TO 63
 2 PRINT CHR$(O);
 3 NEXT O

No A or U in this answer. Sinclair ZX80 and ZX81 character codes begin at 38, which is non-ASCII compliant.
Sinclair ZX80 BASIC (only using I), 237 ~73  [tonkenized] BASIC bytes
 1 PRINT CHR$(38);"BCD";CHR$(42);"FGHIJKLMN";CHR$(52);"PQRST";CHR$(58);"VWXYZ"

Nice. You need to add the bytes from programs with no I and no O.

For other solutions, I'll have to use assembly, so I'm thinking about that one, I'll update shortly.

Braingolf, 12 bytes
62g[59gl+]&@

Try it online!
As I have just learned this language, its probably golfable.

Pushy, 4 bytes
Only requires a single program:
26XQ

Try it online!
26X   \ Push range(0, 26), E(X)clusive.
   Q  \ Convert to relative uppercase alphabet letters and print.

Pyt, 1 byte
ɫ

Implicitly prints "abcdefghijklmnopqrstuvwxyz"
Try it online!

Jelly, 7 bytes
”Ø;“b»V

Try it online!
Uses Jelly string compression to get A, prepends Ø to get alphabet from alphabet constant (ØA), and evals.

Gol><>, 9 bytes
`z9sF:M|H

Try it online!

Ahead, 12 bytes
"bz"69M:1-W@

"bz"          push b (98) then z (122)
    69M       push 69 (charcode for E) then evaluate (E = expand range)
       :1-    dup stack top then sub 1 to get a
          W@  print all chars then exit

Try it online!

Vim, 11 bytes
:h<_
jjYZZp

Try it online!
Note: This answer was taken from this tip.

This answer was not mine, but I thought that it should be here since it's basically the shortest way to do it and there's no other Vim answer. Should it be marked as "Community Wiki"?

Stax, 3 bytes
ïΣK

Run and debug it
Little bit cheaty. Unpacks to the following:
Stax, 3 bytes
VAv

Run and debug it
VA  # "ABCD...XYZ"
  v # lowercase

Python 3, 45 bytes
prⁱnt(*mªp(chr,rªngᵉ(97,123)),sᵉp="")

Attempt This Online!
Contains none of the prohibited vowels (proof).
Uses this tip: Python 3 treats certain Unicode characters in identifiers as letters, even though they're not actually the same character. Superscript letters work (3 bytes each), as do the Romance-language ordinal indicators º and ª (2 bytes each).

AWK,35 (using o,i)
END{for(_=0;_++<26;)printf"%c",96+_}

neglected E from the count considering 'E'!='e'
;)

Julia, 12
['b'-1:'z']

Though the output doesn't look all that nice.
26-element Array{Char,1}:
'a'
'b'
'c'
.
.
.
'z'

JS, 43
Run this in the browser's console or nodeJS. Uses no vowels.
Outputs happens in the console.
To output it in the browser, add alert or document.write around it, but it's longer.
"\141bcd\145fgh\151jklmn\157pqrst\165vwxyz"

or
"\x61bcd\x65fgh\x69jklmn\x6fpqrst\x75vwxyz"

beeswax, 28 chars
Just trying out how well beeswax is able to perform in comparison to other languages.
>@5~5.P@>}@Mq
dP(6~4_#dP@#"<

You can clone my GitHub repository, containing the interpreter, written in Julia, the language specs and examples.

Thunno 2, 1 byte
Ạ

Ạ != A. Constant for "lowercase alphabet".
Thunno 2 B, 6 bytes
ṇßæ96>

No symbols that look like vowels here.
Explanation
ṇßæ96>  # Full program
ṇß      # Push compressed integer 122
  æ     # Filter the range [1..122] by:
   96>  #  Greater than 96?
        # Implicit output, converted to
        # characters by the B flag

Normally we would have used "inclusive range" (I), but that's a vowel.
Screenshots

Python 48 chars without a e o u
print'\x61bcd\x65fgh\x69jklmn\x6fpqrst\x75vwxyz'

What about no i? It is surely possible. Something like exec'pr\x69nt...'. Also, the header should say "Python 2", if you want to be exact.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/