text:
Diagonal Alphabet
Given no input, your task is to generate the following:
a
 b
  c
   d
    e
     f
      g
       h
        i
         j
          k
           l
            m
             n
              o
               p
                q
                 r
                  s
                   t
                    u
                     v
                      w
                       x
                        y
                         z

Nonvisually, your task is to generate each letter in the alphabet, with spaces before it equal to its position in the alphabet minus one.
If you print this, it must appear like the above. Extraneous whitespace that does not affect appearance, as well as a trailing newline, is allowed. You can use all lowercase, or all uppercase.
You may also return this from a function as per usual rules, either as a string with newlines, or a list of strings.
This is code-golf, so shortest answer in bytes wins!

Do the spaces need to be real ASCII spaces, or can I give output like a<VERTICAL-TAB>b<VERTICAL-TAB>c...?  How about if there are some backspace characters in there too?  As long as the visual result is the same?

@DigitalTrauma as long as it appears the same, I don't care what kind of whitespace you use.

Can I use tabs instead of spaces?

@yamboy1 hmm, probably not. Most tabs are set to a large number of spaces - if your diagonal looks like it has 4 spaces before the b, it won't look very diagonal. If it looks like the slope is ~-1 then it's fine.

does not affecting appearance include having an extra leading space or 2?

@MistahFiggins sure, as long as they are on every line

Charcoal, 2 bytes
↘β

Try it online!
How?
 β - the lowercase alphabet
↘  - direction

Exactly the kind of challenge for which Charcoal was originally designed.

The right language :)

This reminds me, I should probably work on Crayon some more... I believe ↘"abc ... xyz"q would be the shortest working program. (Try it online!) ↘``26O;)q should work (start with a backtick; for each I in 0...25, pop the implicit I, increment the backtick and output), but it throws an "empty stack" error for some reason...

2 bytes?!  In what encoding is the SOUTH EAST ARROW a single byte?

@Wyck Charcoal (note: speculation) uses a custom code page, which can be compressed to 1 byte instructions. That's legitimate for Code Golf. https://codegolf.meta.stackexchange.com/questions/9428/when-can-apl-characters-be-counted-as-1-byte-each

@Wyck Charcoal custom code page

@Wyck oops, yes I meant to add a link to the code-page via "bytes" in the header!

@Draco18s - thanks

@StephenS, I think you mean the bottom-right language :)

C, 45 bytes
f(i){for(i=0;++i<27;)printf("%*c\n",i,i+96);}

Thanks to @Dennis for saving 5 bytes!

Works on my machine™

I think you'd have to initialize or reset i at some point. At least on TIO, f() only works once.

@Dennis Ah, you're right. Fixed that.

f(i){for(i=0;++i<27;printf("%*c\n",i,i+96));} saves a few bytes.

f(i){for(;++i<28;)printf("%*c\n",i-1,i+95);} saves one byte.

42 bytes: f(i){for(;i<27;)printf("%*c\n",i++,i+96);}

@KritixiLithos That relies on 0 being previously stored in the register used for passing the first argument, which is not always the case, so it doesn't work all the time. Try it online!

(cc @Steadybox)

i;f(){while(++i<27)printf("%*c\n",i,i+96);} saves a few bytes.

@MDXF No, that is essentialy what I had previously and does not work because it renders the function unable to be called multiple times.

Do we have a rule requiring a function to be able to be called multiple times?

@MDXF Yes, we have.

f(i){for(i=96;i<122;)printf("%c\v",++i);} for 41 bytes - make sure to run this on an actual terminal (yes, this is allowed)

Python 2, 36 bytes
n=65;exec"print'%*c'%(n,n);n+=1;"*26

This takes advantage of the extraneous whitespace that does not affect appearance rule.
Try it online!
Alternate version, 38 bytes
n=1;exec"print'%*c'%(n,n+96);n+=1;"*26

This produces the exact output from the challenge spec.
Try it online!

How does %*c even work?

%*<identifier> takes two arguments: the length to pad it to and the actual thing to substitute. Some printf implementations have even more obscure features, such as the %1$<identifier> I used here.

Ruby, 28 bytes
26.times{|a|puts" "*a<<97+a}

Try it online!
Explanation:
The << operator on a string in Ruby does the trick, as explained in the Documentation

str << integer → str

str << obj → str

Append—Concatenates the given object to str. If the object is a Integer, it is considered as a codepoint, and is converted to a character before concatenation.

05AB1E, 14 8 6 bytes
-2 bytes thanks to @Emigna
AvyNú»

How it works
A      # lowercase alphabet
 v     # for letter in alphabet
  y    # push letter
   N   # push index of letter
    ú  # Pad letter with index of letter spaces
     » # Join with stack on newline.

Try it online!
Original version, 14 bytes
26FNð×N65+ç«}»

You can save another 2 bytes with AvyNú».

@Emigna: Thanks! Will edit that in.

ƶ seems so perfect, but it's not :(.

Λ probably wasn't available yet at the time, but 26A3Λ saves a byte.

@KevinCruijssen AgA3Λ was my first thought :P.

@KevinCruijssen didn't even notice my previous comment. So I guess it was technically my second thought xD

@MagicOctopusUrn ₂A3Λ would have been even shorter.

@KevinCruijssen oooo... 26 is a built-in now! Nice call.

Vim, 29 bytes
:h<_↵↵↵y$ZZ25o <Esc>{qqpblD+q25@q

Try it online!
↵ means press the return key
< Esc> means press the escape key
How does this work?
:h<_↵↵↵                             Open the help and navigate to the alphabet
       y$ZZ                         Copy the alphabet and close the help
           25o <Esc>                Abuse auto-indent and create a whitespace diagonal
                    gg              Go to the beginning of the file
                      qq            Record a macro
                        pb          Paste the alphabet and go to the first letter
                          lD        Go to the second letter and cut the rest of the alphabet
                            +       Go to the first non-blank character in the next line
                             q      Stop recording the macro
                              25@q  Run the macro for the remaining letters

Try it online!  You can use this to demonstrate it (V is based on Vim and mostly backwards compatible except apparently autoindent defaults to off).  Also, less important, you missed the + in your explanation which threw me for a second.

Thanks @nmjcman101! I was trying to find some way to try vim online and never knew that about V

You can use ␛ instead of <Esc>.  It looks a little better in my opinion.

You can save one byte if you do { instead of gg

You could use 2↵ instead of ↵↵↵ and maybe Y instead of y$

Thanks @DJMcMayhem! Saved one byte with that.
The reason why I can't use the Y instead of y$ is because it would yank also a newline and would have to delete it after every paste. So it would be similar unless I can think of something else.

@WheatWizard: how do you type your diagonal Esc ? using kbd tag ? Esc

@OlivierDulac I copied it and pasted it.  It is unicode 241B

That's strange. I see that character as an horizontal "ESC". It definitelly looks better in other fonts

R, 38 37 36 bytes
write(intToUtf8(diag(65:90),T),1,26)

(The use of write is inspired by  @Giuseppe's answer.)

I swear I tried that but couldn't get it to work! Well done. You can save 1 byte by using 65:90, since upper case is allowed.

@user2390246 Thanks for pointing out!

you can use 1 rather than "" to shave off another byte.

@Giuseppe Thanks for pointing out!

JavaScript (ES6), 60 59 bytes
f=(n=10)=>n-36?" ".repeat(n-10)+n.toString(++n)+`
`+f(n):""

A recursive function which returns a string with a trailing newline.

Whoa, that's so sneaky. Converting a number in the range 10 to 36 to a number in a weird base. Don't understand yet why the base has to increase too though.

@SteveBennett Because n.toString(n) is always "10" :P (within 2...36, that is)

Yeah, but n.toString(36) gives the right result, for n in 10..35?

@SteveBennett Correct, but n.toString(++n)+f(n) is a byte shorter than n.toString(36)+f(n+1).

You could do f=(n=10,s='')=>n-36?s+n.toString(++n)+'\n'+f(n,s+' '):"" for 55.

Save a byte with some ES8: "".padEnd(n-10)+n.toString(++n).

@Arnauld, f=(n=10,s='')=>n-36?s+n.toString(++n)+'\n'+f(n,s+' '):s would seem to be permissible.

@Shaggy I suppose it is. This doesn't seem to break the rules.

If only a leading newline had been allowed, you could have used f=(n=10,s='\n')=>n-36?s+n.toString(++n)+f(n,s+' '):''.

@Neil even f=(n=10,s='')=>n-36?s+n.toString(++n)+'\n'+f(n,s+' '):'' is shorter

@Shaggy Can't you replace '\n' with a backtick newline?

Yes, @Oliver. I only used \n above because you can't have newlines in comments and the single quotes are because there doesn't seem to be a way to escape backticks in comments.

PHP, 39 bytes
for($s=a;!$s[26];$s=" ".++$s)echo"$s
";

This is rather verbose :) Here's mine

Pure Bash, 13
echo {a..z}^K^H

Here ^K and ^H are literal vertical tab and backspace ASCII control characters.  The xxd dump of this script is as follows - use xxd -r to regenerate the actual script:
00000000: 6563 686f 207b 612e 2e7a 7d0b 08         echo {a..z}..

{a..z} is a standard bash brace expansion to produce a b c ... z (space separated)
the ^K vertical tab drops the cursor down one line to the same position
the ^H backspace moves the cursor back one to erase the separator space

Try it online. col and tac are used in the footer to get this to render correctly in a browser window, but this is unnecessary in a regular terminal.

If the above unorthodox control characters in the output are too much of a stretch for you, then you can do this:
Bash + common utilities, 24
echo {a..z}^K^H|col -x|tac

Here ^K and ^H are literal vertical tab and backspace ASCII control characters.  The xxd dump of this script is as follows - use xxd -r to regenerate the actual script:
00000000: 6563 686f 207b 612e 2e7a 7d0b 087c 636f  echo {a..z}..|co
00000010: 6c20 2d78 7c74 6163                      l -x|tac

Try it online.  The vertical tab and backspace may be rendered invisible by your browser, but they are there (invisible on chrome, visible on firefox).

col -x re-renders the input such that funny control characters are replaced with spaces and newlines to give the same visual result
for some reason col outputs lines in reverse order.  tac corrects that.

That is very cool :)  (and thanks to meta and @Dennis for suggesting sorting answers on codegolf by activity instead of score, to have better answers come up instead of the (very boring) codegolf langages builtins ones : https://codegolf.meta.stackexchange.com/questions/10127/how-can-we-help-users-who-are-put-off-by-the-use-of-golfing-languages#comment32362_10132)

Many terminals render ^K as cursor up, which is the behaviour that col must be emulating here.

@Neil yes, that makes sense - the col manpage calls a VT a "reverse line feed".  xterm, gnome-terminal and OSX terminal all drop down a line though...

V, 15 13 11 bytes
¬azòÙr klDj

Try it online!
Explanation
¬az         ' Insert a-z
   ò        ' Recursively
    Ù       ' Duplicate current line down
     r      ' Replace the first character with a ' '
       kl   ' Move up a line and right
         D  ' Delete from here to the end
          j ' Move back down

Brain-Flak, 124, 116, 106 bytes
((((()))))(((([][]){}){})[[]()]<>){(({})<(({})<({}<>({})({})<>)>)
{({}<(<>({})<>)>[()])}{}(<>[][]<>)>[()])}

Try it online!
Explanation:
This answer abuses the Stack Height Nilad, but in a new way that I've never used before, which I'm pretty proud of. Other than that, the answer's not too clever.
So analyzing the characters used in this ASCII art, there are really three values that are frequently used:

32 (space),
64 (add 64 to N to get the N'th letter of the alphabet), and
10 (newline)

As well as 26. (number of loops) And these numbers are pushed in different locations, so we can't really reuses intermediate values to make the large numbers smaller. And pushing all for of these numbers is a whopping 86 bytes alone:
10:
((()()()()()){})

26:
((((()()()){}){}()){})

32:
((((()()()()){}){}){})

64:
(((((()()()()){}){}){}){})

This is horrible. So here's how we make it more convenient. The obvious approach is to push a 32 onto the alternate stack, which makes our 32 snippet become: (<>({})<>) and our 64 snippet become (<>({})({})<>). If we combine our initial push 32 with our initial push 26, we can save 8 bytes roughly. (my first golf).
But here is where the trick I'm really proud of comes in. Since we're not using the alternate stack for anything else, we might as well golf down the 10 also. To do this, we'll push 4 arbitrary numbers onto the stack right at the start of the program. Since we also push 32, this increases the value of the [] nilad, to 5, which makes our 10 snippet much more convenient. And lucky for us, it actually lets us golf the push 32 and 26 snippet down too!
#Push 32, 26
(((((()()()()){}){}){})<>[(()()()){}])

#Push 10
((()()()()()){})

Becomes
#Push 32, 26 (-2 bytes)
(((((())))))((([][][]){}()())[[]]<>)

#Push 10 (-6 bytes)
(<>[][]<>)

So here is a detailed explanation:
# Push 1 four times
((((()))))

# Push 32 to main stack (to reuse later)...
((([][][]){}()())

# And then 26 to the alternate stack
[[]()]<>)

#While true
{

    # Keep track of the current TOS
    (({})<

        # Push [TOS, TOS + 64] (To get uppercase characters)
        (({})<({}<>({})({})<>)>)

        # TOS times...
        {
            # Decrement the loop counter, while pushing a space underneath it
            ({}<(<>({})<>)>[()])

        # Endwhile, pop zeroed counter
        }{}

        # Push 10 (newline)
        (<>[][]<>)

    # Push TOS - 1 back one
    >[()])

# Endwhile
}

APL (Dyalog), 9 7 bytesSBCS
-2 bytes thanks to ngn's hint.
↑⍨∘-⌸⎕A

[Try it online!][TIO-j3o0ipjy]
⎕A the uppercase Alphabet
⌸ between each (element,list of indices) pair, insert the following tacit function:
 ↑⍨ from the element (the letter) take…
 ∘ the…
 - negated-index number of characters, i.e. that many characters from the back, padding on the front with spaces.
Try it online!

Nice.  My J attempt was quite a bit more verbose.  Is there a translation of these verbs into J?

@Jonah Verbs: ↑ is {. and ⍳ is i. Adverbs: ¨ is "0 and ⍨ is ~.

Thanks.  Looks like the J translation loses some brevity: (a.{~97+i.26){."0~-1+i.26

@Adám the output doesn't look as required; hint: use ⌸ to output a proper matrix and save 2 bytes

@ngn You may also return (…) a list of strings. But I'll investigate. Edit: Oh yes, of course!

@Adám grr, I should read more carefully, the challenge says "If you print this, it must appear like the above." and then contradicts itself

Google Sheets, 67 65 bytes
=ArrayFormula(IF(ROW(A1:Z)=COLUMN(A1:Z26),CHAR(96+ROW(A1:Z26)),))

=ArrayFormula(IF(ROW(A1:Z)=COLUMN(A1:Z26),CHAR(96+ROW(A1:Z26)),""))
Going off the clarification that any whitespace will do, I've used visibly empty cells

Let me know if this doesn't count, if I've misunderstood the byte count or if I've screwed up some etiquette as this is my first post here.
Edit: It turns out I can save 2 bytes by leaving out the "" as Google sheets will accept an empty if value.

Welcome to PPCG :) Looks good! Good job beating the other Google Sheets answer!

Octave, 25 19  or 12? bytes
[diag(65:90)+32 '']

Try it online!
Other solution proposed by  @LuisMendo (12 bytes) that I tested it in windows version of Octave:
diag('a':'z')

Explanation:
Generates diagonal matrix of a:z.

@LuisMendo In tio I can not produce the same result. It is an expression ,that can be evaluated ,that produce the desired result:)

The solution proposed by Luis seems to work on TIO now... New version of Octave maybe?

Or new version of tio!?

Java 8, 72 71 70 61 bytes
o->{for(int a=0;a++<26;)System.out.printf("%"+a+"c%n",a+96);}

-1 byte by outputting the uppercase alphabet instead of lowercase.
-1 byte by printing directly, instead of returning a multiline String.
-8 bytes thanks to @OliverGrégoire by using printf directly to get rid of String s="";. And also -1 byte by changing ()-> to o->.
Try it here.

The naive implementation is shorter than I would have thought. You can save a byte with c=65 (or 64 actually) so you don't need the 3 digit number. Can returning an array instead of the string save you any bytes as you can remove the +"\n"?

@TheLethalCoder Ah, didn't knew we were allowed to output the uppercase alphabet. Skimmed over that. Thanks. And what do you mean by outputting an array? Like an array of arrays?

Just an array of each line: or a list or strings. Although I'm not sure if it'll be any shorter.

@TheLethalCoder Try defining an array, it's really long in Java: String s="",a[]=new String[26]. I wouldn't go that way.

@TheLethalCoder I doubt it will be shorter, because I'll have to initialize the array String[]a=new String[26]; or List import java.util.*;List l=new ArrayList();. I have been able to reduce it by an additional byte by printing directly instead of returning a multi-line String.

@OlivierGrégoire, CC Kevin, I've not used Java so I wouldn't know just thought it was worth noting in case it helped.

@TheLethalCoder Any tip is welcome, so thanks. But in this case it won't be shorter. :)

In that kind of answer, can you have a lambda parameter ? Having any dummy param would save 1 byte. Plus, can you pass the PrintStream as a parameter ? o->o.println("") It would actually make sense with the context, where do you want to print your diagonal.

@Winter About your first suggestion, that's still being discussed in this meta-post, but judging by the votes I guess it's indeed allowed from now on. As for the second I'm not sure.. It kinda feels like cheating/bending the rules, especially after these heated discussions in the comments of this meta post and answers.

62 bytes: ()->{for(int a=0;a++<26;)System.out.printf("%"+a+"c%n",a+96);} using the same idea as in another challenge.

PowerShell, 29 bytes
0..25|%{' '*$_+[char]($_+97)}

I like how you add 97 to $_ as you go, nice.

shortC, 33 bytes
AOI_=0;++_<27;R"%*c\n",_,_+96));}

Try it online!

Alice, 22 20 bytes
52E&waq'a+q&' d&o]k@

Try it online!
Even though the output is a string, it turns out ordinal mode is not the way to go for this challenge.
Explanation
52E&w             k@     do 26 times
     a                   push 10 (LF)
      q                  push current tape position (initially zero)
       'a+               add the ASCII code for "a"
          q&'            push 32 (space) a number of times equal to tape position
              d&o        output entire stack
                 ]       move tape position one space to the right

Previous solution
["za/?rO&
' !]\"ohkw@/

Try it online!
I went through about ten 23-byte solutions before I was able to find this one.
Explanation
This program uses the tape to track the number of spaces to output.  Cardinal and ordinal modes use the same tape, but they have separate tape heads.  The two modes have different interpretations of what they see on the tape, and the program fully exploits that difference.
The commands are executed in the following order:
[                   move cardinal tape position left
 "za"               push this string (as a string, since the final " is in ordinal mode)
     r              interpolate to entire range (i.e., the lowercase alphabet backward)
      h             split first character from string
       &            for each character in string: push that character and...
        w                                         push current address onto return address stack
         ' !        (cardinal mode) place 32 (space) at current cardinal tape position
            ]       (cardinal mode) move cardinal tape position right
             ?      (back to ordinal mode) read string from tape starting at ordinal tape position
                    this string will consist of n-1 spaces.
              o     output string of spaces
               O    output top of stack (current letter) followed by newline
                k   return to pushed return address.
                    after 26 times through this loop, the return address stack will be empty and this is a no-op.
                 @  terminate

Brainfuck, 103 bytes
>-<-----[[<+>->>+++>-<<<]>++]<<<<<<<<<[-]>>>-[<[-]<[-]<[>+>+<<-]>>[<<+>>-]<[>>>>.<<<<-]<+>>>>.+>>.<<<-]

Try it online!
The location of the variables is somehow improvable.
Explanation
>-<-----[[<+>->>+++>-<<<]>++]   Initializes the tape.
<<<<<<<<<[-]>[-]>>-             Resets variables that
                                need to be at 0.
[                               For loop (25 to 0).
 <[-]<<[>+>+<<-]>>[<<+>>-]      Copy the spaces count in
                                order to use it in a loop.
 <[>>>>.<<<<-]                  Prints the spaces.
                                Prints the character followed
 <+>>>>.+>>.<<<-                by a new line. Also decrements
                                the main loop counter.
]

Google Sheets, 69 bytes
=ArrayFormula(JOIN("
",REPT(" ",ROW(A1:A26)-1)&CHAR(96+ROW(A1:A26))))

Nothing complicated here. The only trick is using ArrayFormula and ROW(A1:A26) to return 26 different values for the JOIN function. Output looks like this:

I think Excel 2016 can do the same thing with TEXTJOIN but I can't enter array formulas in the online version and only have 2013 myself. The formula should be this:
=TEXTJOIN("
",FALSE,REPT(" ",ROW(A1:A26)-1)&CHAR(96+ROW(A1:A26)))

Entering it as an array formula (Ctrl+Shift+Enter) adds curly brackets { } on both sides, bringing it to 67 bytes. Anyone who can verify it works is welcome to use it as their own answer.

Jelly,  10  9 bytes
-1 byte thanks to Dennis (avoid decrementing J by using a lowered range, 26Ḷ, directly)
26Ḷ⁶ẋżØaY

A full program that prints the result.
Try it online!
(ØaJ’⁶ẋż for 7 is a monadic link that returns a list of lists of lists of characters, but that is like [["a"],[" ","b"],["  ","c"],...] which is probably unacceptable.)
I would, however, not be surprised if there was a shorter way I have not thought about!
How?
26Ḷ⁶ẋżØaY - Main link: no arguments
26        - literal 26
  Ḷ       - lowered range = [0,1,2,...,26]
   ⁶      - literal space character
    ẋ     - repeat          [ [],      [' '],      [' ',' '],    ...,  [' ',' ',...,' ']]
      Øa  - yield lowercase alphabet
     ż    - zip             [[[],'a'],[[' '],'b'],[[' ',' '],'c'],...,[[' ',' ',...,' '],'z']]
        Y - join with newlines  [[],'a','\n',[' '],'b',\n',[' ',' '],'c','\n',...,'\n',[' ',' ',...,' '],'z']
          - implicit print (smashes the above together, printing the desired output)

I'd even allow [["a"],[" ","b"],[" "," ","c"],...] since a list of chars is an alternative definition for a string, but a tuple doesn't seem to fit :)

Yeah that's what I thought.

...note that in the above each "..." is a list of chars, so really it's [[['a']],[[[' '],['b']],[[' ',' '],['c']],...] since Jelly has no strings, just lists.

26Ḷ⁶ẋżØaY saves a byte.

ØaJ’⁶ẋż for 7, for your alternative version.

@Dennis Thanks - I do kind of think there must be a 6 or 7 byter out there...

@LeakyNun, oh yeah LCC...

Seed, 6014 bytes
I don't think this will win any awards, but just for fun, here's a solution in Seed.
86 [encoded data, 6011 characters]

It translates to the following Befunge program:
vaa{       @>
v#      g02<v
>30g20g`   |
10g-:!v!: < >#<
v,:g02_40g,1- ^
>1+20p$91+, v

brainfuck, 80 bytes
++++++++[>+>++++>++++++++>+++<<<<-]>++>>+>++[->[<<<.>>>->+<]>+[-<+>]<<<.+<<.>>>]

Try it online!
Formatted:
++++++++[>+>++++
>++++++++>+++<<<
<-]>++>>+>++[->[
<<<.>>>->+<]>+[-
<+>]<<<.+<<.>>>]

Uses a simple multiplicative generation function to put some constants in memory, then repeats the process of printing N spaces then 'A' + N for N = 0..25.
Annotated:
INITIALIZE TAPE: 10 32 65 >26< 0 0
C_NEWLINE: 10
C_SPACE: 32
V_ALPHA: 65
V_COUNTER: 26
V_PREFIX: 0
V_PREFIX_TEMP: 0
++++++++[>+>++++>++++++++>+++<<<<-]>++>>+>++

WHILE V_COUNTER != 0  [-
   "PRINT C_SPACE REPEATED V_PREFIX TIMES"
   "V_PREFIX_TEMP = V_PREFIX"
     V_PREFIX TIMES  >[-
       PRINT C_SPACE <<<.>>>
       INCREMENT V_PREFIX_TEMP >+<
     ]
   "V_PREFIX = V_PREFIX_TEMP PLUS 1"
     V_PREFIX_TEMP PLUS 1 TIMES  >+[-
       INCREMENT V_PREFIX <+>
     ]
   PRINT C_ALPHA <<<.
   INCREMENT C_ALPHA +
   PRINT C_NEWLINE <<.
>>>]

brainfuck, 121 bytes
+++++++++++++[>+++++>++<<-]+++++[>>>++<<<-]++++[>>>>++++++++<<<<-]>>>>>-<<<[>>>+[>+>+<<-]>[<<.>>-]>[<<+>>-]<<<<<<.+>>.<-]
Try It Online!
I'm new to golfing and I know this is extremely golfable but I just learned brainfuck and wanted to see if I could actually do something with it, so I'm sorry that this isn't an impressive answer.

Perl 5.28.1 (webperl) + -l013, 14 bytes
print for a..z
Try it online!

Perl 5 + -l, 21 bytes
$\.=$",print for a..z

Try it online!

><>, 46 44 42 bytes
"A"0::?!v" "o1-40.
*(?!;30.>~$:oao1+$1+:d2

Try it online!
Explanation
Line 1:
"a"0::?!v" "o1-40.
"a"0                       :Initialize the stack items (print char and space count)
    ::?!v                  :Duplicate the space count, check if 0, go down if 0
         " "o1-            :Print a space then take 1 from the space count
               40.         :Jump to codepoint row 0 col 4 (this restarts the loop)
Line 2:
*(?!;30.>~$:oao1+$1+:d2
        >~                 :Remove the zeroed space counter off the stack
          $:oao1+          :Place our print char on the top of the stack, duplicate and print it, print a new line, increase it by 1; a->b->c etc
                 $1+       :Place our space count on the top of the stack and increase it by 1
*                   :d2    :Duplicate the space counter, add 26 to the stack
 (?!;                      :Add 0 to the stack, less than compare 0, if the counter is above 0 it terminates
     30.                   :Jump to the first line, (back to printing spaces)

This is a completely different take from my previous 46 bytes so I've included the TIO to the only one as well.
46 bytes Try it online!
Below is a link to Emigna's submissions, it was the first ><> answer but I believe mine is different enough (and saves a few bytes) to warrant a second one.
Emigna's answer

And now we're tied. Best if you golf off a byte or two to be sure ;)

@Emigna, I thought 3 saved bytes would be enough :o guess I have some more work to do :)

R, 59 49 47 bytes
-10 bytes thanks to djhurio
-2 bytes thanks to Sven Hohenstein

write("diag<-"(matrix("",26,26),letters),"",26)

Prints to stdout. Outgolfed by user2390246
Try it online!

You can replace 26^2 with 676 to save a byte.

m=matrix("",26,26);diag(m)=letters;write(m,'',26) (49 bytes)

For the same amount of bytes, you can print the matrix using cat(m,fill=27)

@djhurio "For the same amount of bytes"

thanks guys! I clearly don't do much with matrices in R, lol.

47 bytes: write("diag<-"(matrix("",26,26),letters),"",26)

@SvenHohenstein I see that that works and I'll be sure to use it but why does it work..?

@Giuseppe The command "diag<-"(x, y) is similar to diag(x) <- y. The value is not assigned to a variable but returned.

@SvenHohenstein That is dark magic indeed!

@SvenHohenstein I was more wondering why R interprets "diag<-"() as a function call. is it just the parentheses? Guess I still have a lot to learn. (It also works with diag<- in backquotes rather than quotes but that still doesn't answer my question)

@Giuseppe Yes, it is because of the parentheses. Without them, "diag<-" is just a string.

Add++, 1069 bytes
+97
&
-87
&
+22
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+66
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-88
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+22
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+67
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-89
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+76
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-98
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+22
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+77
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-100
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+83
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+84
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-106
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+87
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+90
&
P

Try it online!
Yep. That is hardcoded. I'm sure there is a better way, and if you want to find it, go ahead, but this way seems to work the best as Add++ is difficult to work with memory.

The TIO link does not work (interpreter says Fatal error: InvalidSyntaxError line 2: '&' InvalidSyntax)

@astroide This was written in Add++ v0.1, and so no longer works (or is the shortest) in the current version. To run it as it was: Try it online! Thanks for reminding me about this post tho, I'll update it at some point

Haskell, 66 65 58 57 45 43 bytes
Thanks to @nimi and @maple_shaft for saving 12 14 bytes.

unlines[(' '<$['b'..n])++[n]|n<-['a'..'z']]

Try it online!

You would get the same score but sometimes you can use <$ instead of replicate: (' '<$[1..(fromEnum n-97)])

You can change @maple_shaft's suggestion to (' '<$['b'..n]).

As unnamed functions are allowed, there's no need for the f=.

Btw, same byte count: ['a'..'z']>>= \n->(' '<$['b'..n])++[n,'\n'].

PHP, 23 bytes
Note: uses IBM-850 encoding.
<?=join(~¶,range(a,z));

Run like this:
echo '<?=join(~¶,range(a,z));' | php -n;echo
# With default (utf8) terminal:
echo '<?=join("\v",range(a,z));' | php -n;echo

Explanation
Create an array of all characters of the alphabet, join it with a vertical tab as glue.

k, 21 bytes
`0:`c$32+(65+!26)*=26

Try it online.
Explanation:
                  =26 /identity matrix of length 26
         (65+!26)*    /for i in {0..25}:
                      /    matrix[i] *= 65 + i
      32+             /add 32 to everything
                      /    turns 0's into spaces
                      /    brings us to a lowercase alphabet for the rest
   `c$                /turn to characters
`0:                   /write to stdout/stderr

An equivalent version in k4 is -1@(-1-!26)$'$.Q.a;; although since the question allows returning a list of strings, (-1-!26)$'$.Q.a should be valid as well.

VBA, 35 Bytes
Anonymous VBE immediate window function that takes no input and outputs the alphabet, diagonally, to the VBE immediate window
For i=0To 25:?Spc(i)Chr(97+i):Next

-2 Bytes thanks to @Chronocidal

Alternatively, 76 50 46 Bytes
Anonymous VBE immediate window function that takes no input and outputs the alphabet, diagonally, to the range [A1:Z26] on the VBE immediate window function
[A:Z]="=If(Row()=Column(),Char(64+ROW()),"""")

You can save 3 bytes by changing Space(i);Chr(97+i) to Spc(i)Chr(97+i)

@Chronocidal - you are absolutely correct - this answer dates back to when I was having some issues with spc() vs space() - Did you know that Space(n) can be assigned to a variable while Spc() cannot?

Oh and @Chronocidal you seem to do a lot of work with VBA, so if you haven't already, you might want to check out the Tips for golfing in VBA page.

RProgN 2, 5 bytes
aS`\x0B.

\x0B is a Vertical Tab Literal
This just takes the lowercase alphabet, splits it, and joins it with vertical tabs. This produces the intended effect on certain Bash Terminals.

Gforth, 45 Bytes
: X CR 26 0 DO i SPACES i 97 + EMIT CR LOOP ;

Explanation
Gforth doesn't allow interpretation of loops, so I had to define a new word X.
: X                 \ Define new word X
   CR               \ Go to a new line
   26 0 DO          \ Loop from 0 to 25
   i SPACES         \ Print i spaces
   i 97 + EMIT      \ Calculate ASCII-code and print it
   CR               \ Next line
;                   \ End of word definition

Try it online!

Welcome to PPCG!

Kotlin, 36 35 bytes
Saved a byte by removing comma (lambda outside of call.)
{List(26){" ".repeat(it)+('a'+it)}}

Try it online!

PowerShell, 29 26 bytes
'a'..'z'|%{' '*($_-97)+$_}

Try it online!
Output:
a
 b
  c
   d
    e
     f
      g
       h
        i
         j
          k
           l
            m
             n
              o
               p
                q
                 r
                  s
                   t
                    u
                     v
                      w
                       x
                        y
                         z

Welcome! There is the more correct answer - https://codegolf.stackexchange.com/a/125139/80745

@mazzy Thanks for letting me know. I tried to look through and find one but must've missed it! However I don't believe it's more correct. Same length, they just used lowercase, which case was said doesn't matter. Could you explain? Thanks!

You are right, I wasn't precise enough. That solution is closer to the task definition.  It is matter if lengths are equals.

@mazzy How about this one? I think I won now :P

Cool! It would be good to point out Powershell 6+

Vyxal rj, 8 7 5 bytes
Thanks to lyxal for -1 bytes.
kaƛC꘍

Try it Online!
There's a... couple leading spaces per line.
Explanation:
ka     # Lowercase alphabet
  ƛ    # For each:
   C   #   Convert to ordinal value
    ꘍  #   Prepend that many spaces
       # 'j' flag - join top of stack with newlines and print

7 bytes

Brachylog, 16 bytes
Ạ;I∋₎C∧Ṣ;Ij₎wCẉ⊥

Try it online!
Explanation
Ạ;I∋₎C             C is the Ith character of "abcdefghijklmnopqrstuvwxyz"
      ∧Ṣ;Ij₎       Juxtapose " " I times
            w      Write to STDOUT
             Cẉ    Writeln C to STDOUT
               ⊥   False: try another C

J, 28 bytes
([,{&a.@+&97@#)@#&' '"0 i.26

pretty:
([ , {&a. @ +&97 @ #) @ #&' ' "0 i.26

Welcome on the site! While there is no obligations to do so, feel free to add some explanations and maybe a link to an online interpreter where we can test your answer (like Tryitonline for instance).

You can save a byte by using "+i.26 instead of "0 i.26

C#, 82 bytes
using System.Linq;()=>Enumerable.Range(0,26).Select(i=>"".PadLeft(i)+(char)(i+65))

Works by creating an array of ints from 0 - 25, creates a string of i length of only spaces. Then adds a char onto the end corresponding to an upper case letter. It lastly implicitly returns an array, in this case an IEnumerable<string>, of each line.

><>, 50 49 46 45 38 bytes
0>:5d*+oao:64*)?;1+:191.
?v84*o:{1+:}(

Try it online!
Explanation
0>          # initialize outer counter and start outer loop
:5d*+oao    # add outer counter to 65 and print as ascii followed by a newline
64*)?;      # if outer counter is greater than 24, end program
1+:1        # increment outer counter and initialize inner counter
91.         # jump to inner loop
:}(?v       # if inner counter is greater than outer counter go back to outer loop
84*o        # else print a space character
:{1+        # and increment inner counter

Your TIO link has an extra > command on the first line but also having a quick look; move the . on the second line to the end and you can then remove the space on the last line for -1 byte :)

@Tealpelican: Thanks for the suggestion. I did some other changes that saved a byte, but I will check if your suggestion might have saved me more :)

MATL, 5 bytes
2Y2Xd

Try it online!
Explanation
2Y2    % Predefined literal: 'a':'z'
Xd     % Diagonal matrix. Implicit display

R, 40 bytes
write(c("",LETTERS)[diag(1:26)+1],"",26)

Try it online
                    diag(1:26)+1           # Create a matrix of ones with 2:27 on the diagonal
      c("",LETTERS)                        # Create a vector containing an empty string followed by the alphabet
      c("",LETTERS)[diag(1:26)+1]          # Use that vector as a lookup table for the matrix
write(                           ,"",26)   # Print over 26 columns

Use of write() copied from @Giuseppe's answer, but uses a different approach to creating the matrix.
Outgolfed by Sven Hohenstein

Python 2, 42 bytes
Out-golfed... by Dennis, no less... ><
lambda:[' '*n+chr(n+65)for n in range(26)]

Try it online!

Any reason why you chose uppercase over lowercase?

@LeakyNun First number I tried and I had to leave.

Brachylog, 17 bytes
25⟦{;Ṣj₍}ᵐ;Ạzcᵐẉᵐ

Try it online!

q/kdb+, 26 22 bytes
Solution:
-1(!:[26]#'" "),'.Q.a;

Example:
q)-1(!:[26]#'" "),'.Q.a;
a
 b
  c
   d
    e
     f
      g
       h
        i
         j
          k
           l
            m
             n
              o
               p
                q
                 r
                  s
                   t
                    u
                     v
                      w
                       x
                        y
                         z

Explanation:
Joins each letter of the alphabet with an increasing number of spaces. Brackets are used due to right-to-left evaluation.
-1(til[26]#'" "),'.Q.a; / ungolfed solution
-1                    ; / print to stdout and swallow return value
                  .Q.a  / shorthand for abc..xyz
                ,'      / concatenate (,) each-left/each-right (')
  (            )        / do all this together
          #'" "         / take each-left/each-right (space)
   til[26]              / range of 0..25

Go, 97 bytes
package main;import."strings";func main(){for i:=0;i<26;i++{println(Repeat(" ",i)+string(i+97))}}

Definitely not the best language to golf with but wanted to get my first solution up, also should note this prints to stderr but I assume that's okay if it's not specificed
Go (as far as I know) lacks the ability to specify a dynamic width for padding formatted strings which is why I had to bring in and use strings.Repeat()
Readable version:
package main

import . "strings"

func main() {
    for i := 0; i < 26; i++ {
        println(Repeat(" ", i) + string(i+97))
    }
}

Welcome to PPCG! Yup, STDERR is OK. Nice first post, I'm out of upvotes for the day :/

No problem, thanks for the welcome @StephenS :) - I don't know if this is the best place to ask but I was looking on tryitonline and people seem to use the header/footer parts for stuff like imports, is that valid for all/most submissions? would probably save me a lot of bytes on Go stuff

uhhh I don't know, try asking on meta, sorry

Ohm, 10 bytes
αß:^MüL;_,

Try it online!
Explanation
αß:^MüL;_,
αß          # Pushes [a-z]
  :         # For each...
   ^MüL;    # Print index amout of spaces
        _,  # Prints the char

I think this is the wrong challenge :) did you mean this one? https://codegolf.stackexchange.com/questions/125104/cartesian-product-of-two-lists

Yep you're right xD. Probably had the wrong tab open

Updated the code to something that actually does this challenge

Python 3, 41 bytes
for n in range(26):print(" "*n+chr(n+97))

You can save 2 bytes by using Python 2

Perl: 23 bytes
22 + 1 for -E flag.
say$"x$i++,$_ for a..z

Usage:
perl -E 'say$"x$i++,$_ for a..z'

Common Lisp, 58 bytes
(dotimes(i 26)(format t"~v@a~%"(1+ i)(code-char(+ i 97))))

Try it online!

J, 19 16 bytes
u:32+(*=)65+i.26

Try it online!

Yabasic, 49 bytes

Another basic answer which takes no input and outputs to the console.
For i=0To 25
For j=1To i?" ";Next
?Chr$(65+i)Next

Try it online!

brainfuck, 64 bytes
+[[-<+>>++<]>]<<++[>[-<<<.>>>>+<]>+[-<+>]<<<+.<<---.+++>>>-----]

Try it online!
Prints in uppercase with a trailing newline.
Initialises the tape to 2N, and uses the 16(-3) as the newline, the 32 as the space, the 64 as the start of the uppercase alphabet, the 128(+2) as the counter (-5 each loop), and the cell at the end as the space counter.

SmileBASIC 3, 33 bytes
FOR I=0TO 25?" "*I+CHR$(97+I)NEXT

Looks like 12Me hasn't answered this one yet…

Assembly (nasm, x64, Linux), 62 59 55 45 + 8 bytes
func:
  ; R8 is the buffer the function will write the output to.
  ; most GPRs must be 0'd!
  mov al, 'a'
  inc edx
  or r8, buf ; Suprise! It's more efficient to write it this way, the equivilent mov requires 3 bytes of padding to follow.
.append:
  mov byte [r8+rbx], al
  mov byte [r8+rbx+1], 0Ah
  add ebx, 2
  cmp al, 'z'
  je .exit
  inc eax
  mov ecx, edx
  inc edx
.dospaces:
  mov byte [r8+rbx], ' '
  inc ebx
  ; cx is used here. Be aware!
  loop .dospaces
  jmp .append
.exit:
  ret

Try it online!
I spent a fair while doing this one. Seriously, some things will slowly drive you insane.
This function outputs a buffer containing the requested data. Said buffer is in the .bss section.
NOTE: It doesn't seem to work on TIO for some reason. Works perfectly fine on my laptop. I built it using the following commands:
nasm -felf64 diagonal-alphabet_125117.s
gcc diagonal-alphabet_125117.o -no-pie

For your viewing pleasure, the TIO version is modified to use the data section instead, so it actually runs.
The bytecount is currently based on the bytecount of the function and the 8 bytes needed to represent the length of .bss
Note to future readers: A CC where most GPRs must be 0'd can be useful, because or is shorter than mov, at least in the case demonstrated above.

Underload, 104 bytes
(z)(y)(x)(w)(v)(u)(t)(s)(r)(q)(p)(o)(n)(m)(l)(k)(j)(i)(h)(g)(f)(e)(d)(c)(b)(a)(
)(:S( )*~S):*::*:*::***^

Try it online!
The snippet :S( )*~S has the meaning:

Duplicate and print the TOS
Add a space to the TOS
Print the string under the TOS

If the TOS starts as a newline and the strings on the stack form the alphabet (with a highest), then executing this snippet 26 times generates the correct output.

Kotlin, 39 bytes
{('a'..'z').map{" ".repeat(it-'a')+it}}

Lambda returning a list of lines.
Try it online!
{                                  // lambda; implicitly return
    ('a'..'z').map {               // map over the lowercase alphabet
        " ".repeat(it - 'a')       // repeat space by letter position
                             + it  // append letter
    }
}

MathGolf, 10 7 bytes
▄{ï *▌p

Try it online!
I'm happy to announce that MathGolf now has a 1-byte literal for the lowercase alphabet! That should make any challenge related to the alphabet a lot easier!
Explanation
▄         Push alphabet as string
 {        For-each
  ï *     Push " "*(loop counter)
     ▌    Prepend to the character
      p   Print

C (gcc), 37 bytes
f(i){for(i=2912;i++%113;printf(&i));}

Inspired by @NieDzejkob; needs to be run on a little endian ASCII machine from a terminal supporting vertical tabs.
Try it online!

i386 Bootsector, 19 bytes (Technically 512 due to padding)
Here is a hexdump of the program without padding:
0000-0010:  b4 0e b3 61-88 d8 cd 10-b0 0a cd 10-fe c3 80 fb  ...a.... ........
0000-0013:  7b 75 f1                                         {u.

And here is the original assembly:
mov ah, 0x0e
mov bl, 'a'
l:
    mov al, bl
    int 0x10
    mov al, 0xa
    int 0x10
    inc bl
    cmp bl, '{'
    jne l

Very simple. Diagonal works by printing a newline without a carriage return.

Rust, 59 bytes
for(i,l)in('a'..'{').enumerate(){println!("{l:>i$}",i=i+1)}

Welcome to Code Golf, and nice answer!

56 bytes

Vyxal 3 j, 5 bytes
nƛmꜝ«

Try it Online!
Woah a Vyxal 3 Answer!

QBIC, 27 bytes
[26|?space$(a-1)+chr$(a+96)

Explanation
[26|          FOR a = 1 to 26
?space$(a-1)  PRINT a-1 spaces (SPACES$ is a QBasic function that prints x spaces)
+chr$(a+96)      and a char representation of a+96

Tcl, 52 bytes
set i 96;time {puts [format %[incr j]c [incr i]]} 26

time is really a tool for measuring time spent, but it's also handy for repetition of code. Indentation and letter are advanced in each iteration.
Ascii code i needs preset to one-before-first-letter, j will be auto-set to 1 on first incr.
If run in an interactive tclsh, the time would also output timings, but if the line is in a script, then it's silent, except for the diagonal.

ZX Spectrum BASIC, 29 bytes
FOR i=NOT PI TO VAL "25": LPRINT TAB i;CHR$ (i+VAL "97"): NEXT i

Numeric literals carry a 6-byte penalty, so using VAL saves me 3 bytes (VAL is a 1-byte token). Note: The ZX Spectrum's output area is only 22 lines high, so I'm sending the output to the printer instead.

Scala, 41 bytes
('a'to'z').map(a=>println(" "*(a-'a')+a))

Previous answer: 45 bytes
(0 to 25).map(a=>printf("%s%c\n"," "*a,97+a))

It is 1 byte shorter than
(0 to 25).map(a=>println(" "*a+(97+a).toChar))

Try it online!

Here is a 37 bytes solution: 'a'to'z'map(c=>println(" "*(c-97)+c))

Pyth, 9 8 bytes
.e+*dkbG

Try it online
Explanation
.e     G  For each element of 'abc...z'...
   *dk    Take a string of spaces with length equal to the index...
  +   b   Add the letter.

0 indexing really helps for this, doesn't it?

I'm two months late, but you can take out the j because outputting as a list is allowed.

@clap Improvements are always welcome.

Japt, 10 9 bytes
Saved 1 byte thanks to @Shaggy
;C£RiXiYî

Run it online!
Explanation:
;C£RiXiYî
;C          // Lowercase alphabet
  £         // Map; At each char:
   R        //   Newline
    iX      //   Insert: X (Iterative char)
      iYî   //   Insert: " " repeated Y (index) times

By default, i inserts the target char at index 0. So, RiXiYî becomes Yî +X+R.

;C£RiXiYî for 9 bytes.

;C¬£XiYç with -R also works for 9.

A short cut for mÈ would allow for an 8 byte solution ;)

I imagine this wasn't available then but 7 bytes ;C¬Ëù°E

Bash, 38 36 35 bytes
printf "%*s
" `echo $[++i]\ {a..z}`

Try it online!
2 bytes less thanks to @DigitalTrauma
1 byte less thanks to @NahuelFouilleul
"%*s\n" takes padding as an argument.
$((++i))\ {a..z} for each letter increment and prepend i plus space (arithmetic expansion)

Replace $(( )) with $[ ].

If another user suggests an edit that improves your score and you use it, it is usual to credit that user in your answer - Thanks!

I don't know if newline is counted as two characters or one, in that case \n can be replaced with new line

Nano, 186 77 bytes
M- represents the alt key
M-ia
 b
 c
 d
 e
 f
 g
 h
 i
 j
 k
 l
 m
 n
 o
 p
 q
 r
 s
 t
 u
 v
 w
 x
 y
 z

Explanation
I've seen a few Vim answers on this site so I thought I would do a nano answer.  Its not nearly as terse as the Vim answers but its still better than typing out the whole thing.
This is pretty simple (a lot simpler than my original answer). M-i sets the auto-indent on.  This means that every line will copy the indentation of the last.  So we start with a and every line add a space and a letter all the way through.

T-SQL, 63 bytes
DECLARE @ INT=0a:PRINT SPACE(@)+CHAR(@+65)SET @+=1IF @<26GOTO a

Written more conventionally, that would be:
DECLARE @ INT=0
a:
    PRINT SPACE(@) + CHAR(@+65)
    SET @ += 1
IF @<26 GOTO a

Tested and working on SQL Server 2012.

Mathematica, 39 Bytes
Grid@DiagonalMatrix@Alphabet[]/. 0->" "

This has trailing whitespace.
Explanation:
                    Alphabet[]          - Create a list of the alphabet
     DiagonalMatrix@                    - Use that as the diagonal of a matrix
                              /. 0->" " - Replaces the 0's with whitespace
Grid@                                   - Then turn it into a 2D grid

Since a list of strings is allowed, and you are not asked to print it or anything, I don't think you need the Grid@.

TI-Basic, 71 69 bytes
"
For(I,1,26
Disp sub(Ans+Ans+Ans+Ans,1,I)+sub("ABCDEFGHIJKLMNOPQRSTUVWXYZ",I,1
End

Don't know how I missed that, thanks for -26 bytes @StephenS

I think you can just do sub(Ans+Ans+Ans+Ans,1,I).

@lirtosiast Thanks, I should have noticed that one.

braingasm, 20 bytes
26[#[32.]97+#+.10.>]

26 times, print (.) a space (32) # (current position on the tape) times; increase cell (+) by 97, then by #; and print the current cell value, along with a newline (10); then go to next cell (>).

AWK, 40 bytes
BEGIN{for(;++i<27;)printf"%"i"c\n",i+96}

Try it online!
I'm curious if there's a shorter way to do this in AWK.

not sure if the rules allow it, but replace BEGIN with END and add 1 char for the needed ctrl-d ?

JAVASCRIPT
Option 1: 59 bytes
a='';for(i=0;i<26;)a+=''.padEnd(i++)+(i+9).toString(36)+`
`

Option 2: 60 bytes
a='';for(i=0;i<26;)a+=' '.repeat(i++)+(i+9).toString(36)+`
`

Option 3: 61 bytes
a='',i=0;while(i<26)a+=' '.repeat(i++)+(i+9).toString(36)+`
`

Option 4: 67 bytes
a='';for(i=0;i<26;)a+=' '.repeat(i++)+String.fromCharCode(96+i)+`
`

Option 5: 68 bytes
[...Array(26)].map(_=>' '.repeat(++i-10)+i.toString(36),i=9).join`
`

easily tested in the browser's console :)

Perl 6, 25 bytes
{" " «x«^26 Z~'a'..'z'}

This function returns a list of the required strings: "a", " b", "  c", ...
^26 is a list of the numbers from 0 to 25.  «x« is the string-replication hyperoperator that maps each element n of its right-hand side to the left-hand side replicated n times, producing the list "", " ", "  ", ....  That list is then zipped with string concatenation (the Z~ operator) with the range of letters from 'a' to 'z'.

R, 56 bytes
for(i in 1:26){cat(rep(" ",i-1),LETTERS[i],'\n',sep='')}

Try it online!
Prints i-1 spaces and the ith letter of the alphabet, plus a newline, 26 times.
Outgolfed by Giuseppe (47 bytes),
user2390246 (40 bytes),
and Sven Hohenstein (37 bytes), but this is the only answer (so far) that doesn't use diag.

Julia, 42 bytes
for i=0:25 println(" "^i,Char[97+i][1])end

Pretty straight forward, print space and character.
Try it online!

Ruby, 18 bytes
puts [*?a..?z]*?\v

Does not work on TIO, link for reference:
Try it online!

Pyth, 11 bytes
j.b+*dNY26G

Explanation:
Try it online!
j.b+*dNY26G   expects no input

j             joins on new line
 .b           for...in loop, uses two iterator variables
   +          joins *dN and Y
    *dN       repeats d (space) N times, where N is one of .b's iterating variables
       Y      another one of .b's iterating variables
        26    the array being iterated for N,.b automatically takes the unary range
          G   initialized to the lowercase alphabet, the array being iterated for Y

SOGL V0.12, 2 bytes
z╝

Try it Here!
z   push the alphabet
 ╝  convert to a diagonal array
    implicitly output as a newline joined string

Pyth, 13 bytes
I've noticed that I've been getting better at these, but Dave or Mr. Xcoder will school me any day of the week.
Update: Pyth tester is down, rip back up.
#p*dt=hZhG=tG

Explanation:
#         Loop until error
 p*dt=hZ  Print without newline: " " times ++Z - 1 (Z defaults to 0) (Could have used + instead of p, but it's easier to explain)
 hG       Implicit print with newline: The first character of the alphabet
 =tG      Remove the first letter in the alphabet variable

Try it online!

Befunge-98 (PyFunge), 30 bytes
1+:0\:'`+\' \k:>:#,_$:'␚-!k@a,

Where ␚ is a literal substitute character
Every line has 3 leading spaces
Try it online!

uBASIC, 36 bytes
Anonymous function that takes no input and outputs to the console.
0ForI=0To25:?Tab(I);Chr$(65+I):NextI

Try it online!

Soon: 100% of alphabet challenge are necromancer'd to the top being called "basic" xD.

@MagicOctopusUrn OH NO!!! You discovered my plot!!

Creating meta-thread to vote on replacing tag "alphabet" with "basic" lmao! Seriously, I love these challenges, but there isn't an alphabet challenge not completed in 05AB1E...  ;_;

Canvas, 2 bytes
ｚ＼

Try it here!

Stax, 6 bytesCP437
åuvÉ◄┘

Try it online!
Explanation
Uses the unpacked format to explain.
Vam]i^)
Va         "abcdefghijklmnopqrstuvwxyz"
  m        For each letter, execute the rest of the program
               Output the result on individual lines
   ]       Change the letter to a single-letter string
    i^     Current loop index+1
      )    Pad the string to given length

Pepe, 79 76 56 bytes
Way better, faster algorithm which performs like 3 times less operations. And saves 3 bytes. Now even more, because Pepe supports flags - no more unnecessary item movement!
REeEEEEeEErEeEEeeeeEREEreeereeErEEEEERrEeeEeeeeerEEEeRee

Try it online!
Explanation
REeEEEEeEE   # push "{" to R
rEeEEeeeeE   # push "a" to r

REE # label "{"

  reee # print stack contents
  reeE # print newline

  rEEEEE       # increment the letter
  R rEeeEeeeee # prepend a space
  rEEEe        # r pointer to end

Ree # goto "{" if the letter didn't reach "{" yet

PowerShell, 35 bytes
$i=97;0..25|%{" "*$_+[char]$i;$i++}

Try it online!
Pipes an array of 0 through 25 to ForEach-Object, which cycles through ascii codes and prefixes with a space multiplied by an incrementing variable.

Roll the [char] calculation into the loop variable for 29 bytes -- Try it online!

Mouse-2002, 43 bytes
(A.Z1+<^A.B:(B.^" "B.1-B:)A.97+!'"!"A.1+A:)

Needs to be run in the Mouse-2002 Interpreter REPL.
Working interpreter can be found here.

Python 3, 51 bytes
print("\n".join(" "*n+chr(n+97)for n in range(26)))

you can avoid the join stuff by putting all this in a comprehensive list [print(" "*n+chr(n+97))for n in range(26)]

K4, 18 bytes
Solution:
-1(-1-!26)$'$.Q.a;

Example:
q)k)-1(-1-!26)$'$.Q.a;
a
 b
  c
   d
    e
     f
      g
       h
        i
         j
          k
           l
            m
             n
              o
               p
                q
                 r
                  s
                   t
                    u
                     v
                      w
                       x
                        y
                         z

Explanation:
Left-pad the alphabet:
-1(-1-!26)$'$.Q.a; / the solution
-1               ; / print to STDOUT, swallow return
             .Q.a  / "abcdefghijklmnopqrstuvwxyz"
            $      / string, basically 1#'
          $'       / pad ($) each-both
  (      )         / do together
      !26          / range 0..25
   -1-             / subtract from -1

Bonus:
15 bytes returning a list of strings rather than printing to STDOUT:
(-1-!26)$'$.Q.a

QBasic 1.1, 35 bytes
FOR S=0TO 25
?SPC(S)CHR$(S+97)
NEXT

-8 thanks to DLosc.

Z80Golf, 19 bytes
00000000: c661 ff3e 0aff 3e20 0c41 ff10 fd79 fe1a  .a.>..> .A...y..
00000010: 20ee 76                                   .v

Try it online!
Disassembly:
restart:
  add 'a'
  rst $38
  ld a, '\n'
  rst $38
  ld a, ' '
  inc c
  ld b, c
k:rst $38
  djnz k
  ld a, c
  cp 26
  jr nz, restart
  halt

brainfuck, 74 bytes
++++++++[->+++>+>++++++++>++++<<<<]>++>++<[->>>>[-<.>>+<]+>[-<+>]<<<+.<.<]

Try it online!
Explanation
++++++++[->+++>+>++++++++>++++<<<<]>++>++ Initialize tape:
26(letter count) 10(lf) 64("A" minus 1) 32(" ") 0(space count) 0(temp)

<[                                        for each letter count
  -                                       decrement letter count
  >>>>[-<.>>+<]                           for each space count print space and move value to temp
  +                                       increment space count
  >[-<+>]                                 add temp to space count
  <<<+.                                   increment and print letter
  <.                                      print lf
  <                                       go to count
]

><>, 35 Bytes
0::?\~1+:8c*+oao:55*)?;!
-10.\84*o1

Try it online
0                         initialise counter
 :                        make a copy to count spaces
  :?\                     only keep looping if greater than 0
    \84*o                 output a space
-        1                decrement the inner counter
 10.                      jump back to the start of the inner loop
     ~                    delete the inner loop counter
      1+                  increment the outer counter
        :8c*+o            make a copy of the counter, add 96, output the character
              ao          output a newline
                :55*)?;   terminate if the counter is now 26 or higher
                       !  skip the 0 at the start of the line

Pascal (FPC), 56 bytes
Well, I found 2 programs with the same number of bytes.
Program 1:
var c:char;begin for c:='a'to'z'do writeln(c:ord(c))end.

Try it online!
Explanation:
var c:char; //declare c as char variable
begin
  for c:='a' to 'z' do //iterate in a loop, c is getting values from a to z
    writeln(c          //write the current character followed by a newline
             :         //with a width of
              ord(c))  //ASCII code of the current character
                       //(using extraneous whitespace allowed by the challenge)
end.

Program 2:
var i:byte;begin for i:=97to 122do writeln(chr(i):i)end.

Try it online!
Explanation:
var i:byte; //declare i as integer variable in range 0..255
begin
  for i:=97 to 122 do //iterate in a loop, i starts from 97 and is incremented in each iteration
    writeln(chr(i)    //write character which ASCII codepoint is the current value of i
                  :   //with a width of
                   i) //current value of i
                      //(using extraneous whitespace allowed by the challenge)
end.

C++ (gcc), 50 48 bytes
[](){for(int c=0;printf("%*c\n",++c,c+97)-27;);}

Try it online!

PowerShell Core, 27 bytes
'a'..'z'|%{' '*(+$_-97)+$_}

Try it online!

Hey Edwin, you can save an extra byte if you remove the + from the +$_-97 statement. Otherwise it's identical to my answer, see Here

Aheui (esotope), 183 bytes (65 chars; 59 Hangul, 6 ASCII)
발밦다빠따반두발따받타빠싺싻삮타빠바파자초
분벋서썩떠번벌또여cbtp어또벓범석터번벋
타타빠싹빠싺밨볺아멓히셕처오져퍼서써섟뻐서

Try it online!

"cbtp" in the middle of the code is just an abbreviation of my nickname, which is ignored by the interpreter and reduce 8 bytes by using ASCII, not Hangul.

Attache, 21 bytes
Output[sp*0:25+$a:$z]

Try it online!
Explanation
Output[sp*0:25+$a:$z]
Output[             ]     write each entry as a line to stdout:
       sp*0:25                spaces repeated 0 to 25 times (array)
              +$a:$z          each followed by a letter from "a" to "z"

Alternatives
22 bytes: Output[" "*0:25+$a:$z]
23 bytes: Print=>(" "*0:25+$a:$z)
24 bytes: Print@{_*sp+NTS@_}=>0:25
31 bytes: Print@&PadLeft=>Zip[$a:$z,1:26]
35 bytes: {Print@_If[$z!in_,$[sp+Succ@_]]}@$a
37 bytes: {Print@_If[_@-1/=$z,$[sp+Succ@_]]}@$a
37 bytes: Print@&PadLeft=>Zip[Chars@alpha,1:26]
40 bytes: Output!ZipWith[PadLeft,Chars@alpha,1:26]
40 bytes: Print=>ZipWith[PadLeft,Chars@alpha,1:26]

05AB1E, 8 4 bytes
₂A3Λ

Try it online!
-4 bytes thanks to @ovs.
₂     # push 26
 A    # push "abcdefghijklmnopqrstuvwxyz"
  3   # push 3
   Λ  # draw a line on an ASCII canvas that is 26 characters long, uses lowercase letters in order for characters, and goes in direction 3 (southeast)

You can use the canvas for 4 bytes: ₂A3Λ

Python 3.8 (pre-release), 60 bytes
n=0
for l in"abcdefghijklmnopqrstuvwxyz":print(" "*n+l);n+=1

Try it online!

This is shorter without an assignment expression: Try it online!

@pxeger Fixed..

Actually, I was wrong; leading spaces are allowed. But it's still shorter this way.

JavaScript (Node.js), 63 bytes
for(i=0;++i<27;){console.log(" ".repeat(i)+(i+9).toString(36))}

Try it online!

Vyxal, 15 14 bytes
₄ʁ(|kaniðn*p,)

Try it Online!

10 bytes

6.125 bytes

Mathematica, 42 bytes
Table[" "~Table~i<>Alphabet[][[i]],{i,26}]

outputs a list of strings

A list of string format is allowed, so you don't need Column@, save 7 bytes. You can save another byte with " "~Table~i. Thanks for letting me know about Alphabet[].

I didn't notice it... thanks for -8bytes

Braingolf, 24 bytes
V# 7-#
R#a[R!&@# >1+v!@]

Try it online!
Explanation
V# 7-#\nR#a[R!&@# >1+v!@]
V                          Create stack2 and switch to it
 # 7-                      Push 32 and subtract 7
     #\n                   Push newline
        R                  Return to stack1
         #a                Push lowercase a
           [............]  Do-while loop, uses stack2 for loop counting
                           Will run 26 times
            R              Return to stack1
             !&@           Print entire stack without popping
                # >        Push space and move it to start of stack
                   1+      Increment letter
                     v     Switch to stack2
                      !@   Print newline

Noether, 52 bytes
"abcdefghijklmnopqrstuvwyxz"~aL(" "i*Pai/P"
"Pi1+~i)

Try it here!
Pushes the alphabet and loops through it, increasing the number of spaces before the character by one each time.

A non competing solution for 26 24 bytes is:
26(" "i*P0Ai/P"
"Pi1+~i)

Try it here!

Aceto, 28 bytes
L 'XcIo
p*=`MILp
aM{'&n
'@dL

Explanation:
First of all, we put the character a in our quick storage ('aM) and set a catch point (@). We then duplicate the top stack element (initially a zero) and load both from quick storage and from the character literal {. These characters are then tested for equality, in which case we exit (=`X).
Otherwise we push a space and multiply it with the previously duplicated stack element (used as a counter). This is then printed, which prints nothing the first time this is run, a single space the second time, and so on (' *p).
We load the current character again and print it, then we load it again, convert it to the number of its codepoint, increment it, convert it to a character again and memorize it (LpLoIcM). Finally, we increment our counter, print a newline, and jump to the catch mark (In&).

Javascript, 75 72 bytes
_=>[...'abcdefghijklmnopqrstuvwxyz'].map((n,i)=>' '.repeat(i)+n).join`
`

3 bytes thanks to Stephen S.

You can save some bytes with backticks and a literal newline for your join: https://jsfiddle.net/pL1onLqb/

Save a byte using some ES8: ''.padEnd(i)+n

Also, outputting the array would seem to be permissible, in which case you can drop the join.

Cheddar, 31 bytes
->(|>26).map(n->' '*n+@"(n+97))

Try it online!
Defines a niladic lambda which returns a list of strings.
Full program, 42 bytes
print(|>26).map(n->' '*n+@"(n+97)).asLines

Try it online!

S.I.L.O.S, 101 bytes
a=26
c=97
lblb
i=0
GOTO d
lblc
print
b-1
i+1
lbld
if b c
b=i+1
printChar c
printLine
a-1
c+1
if a b

Try it online!

LOGO, 47 bytes
Can be tried with FMSLogo. Unfortunately the version at Turtle Academy does not work well.
for[i 0 25][repeat :i[type "\ ]show char 65+:i]

Oracle SQL, 62 bytes
SELECT LPAD(CHR(LEVEL+96),LEVEL) FROM DUAL CONNECT BY LEVEL<27

C# 73 68 bytes (Thanks to raznagul)
I'm pretty new to this. Do I need to include class/main declaration overhead for C#?
Edited to include anonymous function declaration
()=>{for(var x='a';x<123;)Console.WriteLine("".PadLeft(x-97)+x++);};

Welcome to PPCG :) For this challenge (and most) you have two options. Either include the boilerplate (main et al) with what you are doing, or... you can create a function, and return either a list of strings for each row, or a string that, if you printed it, would display correctly.

If you use upper case the while condition changes to x<91 saving 1 byte. And you can save another 2 bytes by removing the {} around the WriteLine-statement.

I've found another 3 bytes that can be golfed away: 1) Use var instead of char. 2) In PadLeft write x-97. 3) Use for instead of while declaring x in the loop: for(var x='A';x<97;)

thanks! I always thought I couldn't use var in a lambda.

Micro, 35 bytes
64:i {i1+:i i c:\
64 26+i=if(,a)}:a a

SimpleTemplate, 66 42 bytes
This simply loops through all characters and outputs them one by one, with newlines and spaces.
{@forfrom"a"to"z"}{@echolV,_}{@setV V," "}

This abuses the automatic variable _ and the automatic flattening of echoed arrays and automatic newline with echol.
Ungolfed: (produces invalid results due to whitespace)
{@for chr from "a" to "z"}
    {@echo indentation, chr, "\n"}
    {@// will create an array like: [[[..., " "], " "], " "]}
    {@set indentation indentation, " "}
{@/}{@// automatically added after the code}

Old version:
There's a repeat function, but I couldn't use it because it's broken.
But this works too.
{@for_ from"a"to"z"}{@incz}{@callstr_repeat intos" ",z}{@echols,_}

Ungolfed: (produces incorrect results due to whitespace added)
{@set z 0}{@//removes warning}
{@for chr from "A" to "Z"}
    {@inc spaces by 1}
    {@call str_repeat into indentation " ", spaces}
    {@echo indentation, chr, "\n"}
{@/}{@// automatically added after the code}

Rexx (Regina), 41 37 bytes
do i=1 to 26
  say right(d2c(96+i),i)
end

Try it online!

Batch, 187 114 bytes
@set s=
@for %%p in (a b c d e f g h i j k l m n o p q r s t u v w x y z)do @call:e %%p
:e
@echo(%s%%1
@set s= %s%

You don't need the @s inside the ()s. Also, you don't need c at all - you can just add a space to s each time. By avoiding setlocal enabledelayedexpansion I got this down to 112 bytes.

I've successfully removed the @s, variable c, and now I couldn't figure out how to echo the variable s without delayedexpansion.

Since you're so close already, here's my 112-byte solution: @set s=&for %%p in (a b c d e f g h i j k l m n o p q r s t u v w x y z)do @call echo %%s%%%%p&call set s= %%s%%.

Modern Pascal 2.0, 43 bytes
for var l:=97 to 122 do write(chr(l),#13);

Explanation
For loop range is the ascii of 'a' to 'z', and the output is converting
the ordinal to character, followed by LF (Line Feed, not CRLF), thus
producing a forward diagonal alphabet. Also, Modern Pascal does not require
the Begin/End block on simple instructions like this.
// Author of Modern Pascal

tcl, 54 47
time {puts [format %[incr i]c [expr $i+96]]} 26

demo

@avl42: mine is longer than yours :P

@avl42: Mine is NOW shorter than yours, using your own poison!

Pyke, 6 bytes
G Foh-

Try it here!
G      -  alphabet
  Foh- - for i in ^:
   oh  -   (o++)+1
     - -  i.pad(" ", ^)

Pyke, 4 bytes
G\J

G   - alphabet
 \J - "\x0B".join(^)

Joins alphabet by vertical tabs

Retina, 93 bytes

aAbBc¶3d¶4e¶5f¶6g¶7h¶8i¶9jA0kA1lA2mA3nA4oA5pA6qA7rA8sA9tB0uB1vB2wB3xB4yB5z
B
¶2
A
¶1
\d+
$*

Try it online!

C#, 82 bytes
var b="";for(int i=0;i<=25;i++){var a=(char)(97+i);b+=new string(' ',i)+a+"\r\n";}

Try it online!

vim 14+16=30 keystrokes
16 keystrokes if you have alpha in nrformats already (I mean, who hasn't?), 30 otherwise.
:set nf=alpha<cr>
ia<esc>
qqYp<c-a>I <esc>q
24@q

Angle brackets denote single characters, e.g. <c-a> is ctrl+a (increment). Actual newlines only for clarity. Seriously, set nf+=alpha is really neat, and it's a feature I've missed in a few specific cases when programming.

Groovy, 40 38 bytes
i=0;("a".."z").each{println" "*++i+it}

Previous solution:
0.upto(25){println" "*it+("a".."z")[it]}

iis used to store the number of spaces that must be printed before each letter. The program iterates through the range "a".."z" (the alphabet), printing each letter with i spaces before it and increments i inline.

Common Lisp, SBCL, 70 bytes
(dotimes(i 26)(format t"~v@t~a
"i(aref"abcdefghijklmnopqrstuvwxyz"i)))

Looping through letters of alphabet and outputting accurate number of spaces before each letter.
another 70 bytes solution:
(format t"~{~26<~a~#@t~>
~}"(coerce"abcdefghijklmnopqrstuvwxyz"'list))

looping through letters and justifying to 26 columns, where word to justify is letter+accurate number of spaces.
building alphabet list using code-char would make it 76 bytes:
(format t"~{~26<~a~#@t~>
~}"(loop as i from 97 to 122 collect(code-char i)))

Swift 3, 75 bytes
for i in 0..<26{print(String(repeating:" ",count:i)+String(i+10,radix:36))}

dc, 53 52 bytes
0si[32Plj1+dsjli>S]sS[0sjlid0<S1+dsi64+dPAP90>M]dsMx

Try it online!
Uppercase because checking that we're below character 90 (Z) is one fewer byte than checking that we're below character 122 (z). Otherwise pretty straightforward: one macro to print spaces and another to call the spacing macro, print the letter, and print a newline.
-1 byte because I forgot to golf my 10 into an A.

Pyth, 9 bytes
m+*;xGddG

Try it online!
The other Pyth approach is golfier because it uses enumerated map, which is 1 byte shorter. I just wanted to post a solution with regular map m, that happens to use the same variable, d as the built-in space. That may be inconvenient, because you cannot refer to the space with d. However, I did a work-around with ;, which gets the global value of the innermost lambda variable.
This returns a list of lines. In order to join them by newlines, we just need to add j in front of the whole code (the link contains the j for readability).
Explanation

jm+*;xGddG  - Full program.

 m       G  - Map over the alphabet with a variable d.
  +         - Add:
   *          - The multiplication of:
     xGd        - The index of the current letter in the alphabet (0-indexed) and
    ;           - Space (which is the global value of d, the innermost lambda
variable).
        d     - The current letter.
j           - Optional: Join by newlines.

QBasic, 54 bytes
SCREEN 12
FOR x=1TO 26
LOCATE x,x
?CHR$(x+96)
NEXT

Explanation
SCREEN 12       Set the screen mode to something that can actially handle > 20 chars on a line
FOR x=1TO 26    Loop from 1 to 26
LOCATE x,x      Set the cursior to the screen position x,x, starting at 1,1 on the top left.
?CHR$(x+96)  Print the current letter of the alphabet
NEXT

Recursiva, 16 15 bytes
{)"P+*-O}97' '}

Try it online!
Explanation:
{)"P+*-O}97' '}
{                - For each
 )               - lower-case alphabet yield 'abc...z'
  "              - Iteration command begin
   P             - Print
    +            - concatenate
     *-O}97' '   - Appropriate number of spaces
              }  - current alphabet (iterate)

C++ (gcc), 73 bytes
As unnamed generic lambda, requires a stream as parameter (like std::cout)
[](auto&O){for(char c=96;++c<123;O<<c<<'\n')for(char w=c-96;--w;O<<' ');}

Try it online!

Pushy, 10 bytes
`a\x26`:"h32}

Where \x26 represents the literal byte 0x26.
Try it online!
`a\x26`         \ Push 'a' and 26
       :        \ Pop 26, loop that many times:
        "       \   Print the stack
         h      \   Increment the letter
          32}   \   Prepend a space

AWK, 40 bytes
BEGIN{for(;i<26;)printf"%"++i"c\n",i+96}

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I didn't see an AWK solution, so here we go. Straightforward implementation, so more golfing may be possible.

Sincalr ZX81/Timex TS1000/1500 BASIC, ~45 tokenized BASIC bytes
 1 FOR I=CODE "A" TO CODE "Z"
 2 PRINT TAB (I-CODE "A");CHR$ I
 3 NEXT I

Some notes; without adding in more bytes to the listing, the standard output to the screen is 32 x 22 only, so when the screen fills, you will need to press C, and the keyword CONT will appear. You will then see the rest of the alphabet.
For those who want to see the Alphabet without having to manually enter CONT each time the last row is hit in the text area, this solution does it for you:
 1 FOR I=CODE "A" TO CODE "Z"
 2 PRINT AT CODE "+",I-CODE "A";CHR$ I
 3 SCROLL
 4 NEXT I

This version costs another 9 tokenized bytes though.

Pyth, 12 bytes
Fb26p*\ b@Gb

There's probably some way I can shave off a couple bytes, but I'm not quite sure yet.
Explanation:
Fb26p*\ b@Gb |
Fb26         | for b in range(26):
    p        |     print(
     *\ b    |           " "*b
         @Gb |                +G[b]

Note: G is initialized to "abcdefghijklmnopqrstuvwxyz"

SNOBOL4 (CSNOBOL4), 72 65 bytes
E	&LCASE O LEN(1) . O @X	:F(END)
	OUTPUT =LPAD(O,X)	:(E)
END

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swapping &UCASE for &LCASE would do the uppercase diagonal instead.

MY-BASIC, 62 bytes
Anonymous function that takes no input and outputs to the console.
For i=0 To 25
For j=1 To i
Print" "
Next
Print Chr(65+I);
Next

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Visual Basic .NET (Mono), 98 bytes
Declared Subroutine that that takes no input and outputs to the console.
Module M
Sub Main
Dim I
For I=0To 25
Console.WriteLine(Space(i)+Chr(65+I))
Next
End Sub
End Module

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Momema, 51 bytes
m01*0w1-9 32 1+*1-1w0w=*1-9+97*0-9 10 0+1*0m=+-26*0

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Explanation:
                                                              #  a = 0
m   0        #  label m0: jump past label m0 (no-op)          #  do {
1   *0       #            [1] = [0]                           #    b = a
w   1        #  label w0: jump past label w1                  #    while b != 0 {
-9  32       #            print chr 32                        #      print ' '
1   +*1-1    #            [1] = [1] - 1                       #      b -= 1
w   0        #  label w1: jump past label w0 (no-op)          #    [end-of-loop jump point]
w   =*1      #  label w2: jump past label w((2 + !![1]) % 3)  #    }
-9  +97*0    #            print chr 97 + [0]                  #    print chr(97 + a)
-9  10       #            print chr 10                        #    print '\n'
0   +1*0     #            [0] = [0] + 1                       #    a += 1
m   =+-26*0  #  label m1: jump past label m((1 + !![0]) % 2)  #  } while a != 0

Python 3,  74 64 63 Bytes
Saved ten bytes thanks to Caird
Saved one byte thanks to Stephen
Changed format to one-liner
Yes there are several Python 2 answers but how about one with Python 3?
for b in'abcdefghijklmnopqrstuvwxyz':print(' '*(ord(b)-97)+b)

First it makes a list of the alphabet then prints each letter but with n (Index of the value) spaces.

64 bytes

41 bytes

I found there's an identical answer here

Mine is a little different

b in 'abc -> b in'abc

Japt -R, 7 bytes
;C¬ËiEç

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PHP, 72 68 67 Bytes
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Try it online (after @Titus review)
Try it online, last review. @Titus Strikes Back
Code, recursive function
function f($v=26){$v&&print str_pad("",$v).chr($v+96)."
".f($v-1);}

Explanation
function f($v=26){
    $v&&print           # if $v not zero then print
    str_pad("",$v)     # pad spaces $v times
    .chr($v+96)     # concat the character at 96+$v
    ."                 # concat a linebreak
    ".f($v-1);          # call the function
}

You need no braces for the echo. 2) Try $l&&print instead of if($l>0)echo. 3) And please don´t use $l as a variable name. ;)

As always, thank you @Titus for your suggestions :D

You´re welcome. print needs no parentheses.

Add++, 43 36 bytes
D,f,@:^,32$yVVL97+
D,g,,26RBF€{f}
$g

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Super suboptimal because I don't know what I'm doing

Java (OpenJDK 8), 58 bytes
a->{for(char b=96;b++<122;a+=' ')System.out.println(a+b);}

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I had no idea that you could make a for loop with a char variable... but here ya go! I’m pretty proud of my solution here, it may be my most golfed submission to date!

Ahead, 31 30 bytes
"az"E>0\:'a-' l
  @?lj:oNW:k\<

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-1 because leading spaces are allowed as long as everything is still aligned.

Python 2, 56 bytes
a=map(chr,range(65,91))
for i in a:print' '*a.index(i)+i

CJam, 13 bytes
26{_S*\'a+N}/

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Explanation
26{        }/  for i in [0..25]:
    S*           puts ' ' * i
   _  \'a+       puts 'a' + i
          N      puts '\n'

Ruby, 43 bytes
(0..25).each{|n|print" "*n;puts (n+97).chr}

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Perl 6, 24 bytes
{map ' 'x$++~*,'a'..'z'}

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Anonymous code block that returns a list of lines.
Alternatively,
{' 'x$++xx㉖Z~'a'..'z'}

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behaves the same for the same bytecount.

C# (.NET Core), 71 58 53 52 bytes
for(var i='A';i<91;)WriteLine("".PadLeft(i-65)+i++);

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Welcome to PPCG! :)

Suggest putting the i++ at the very end to save a byte.

Thanks @JonathanFrech I have included in my new approach

You can replace '[' with 91 for -1 byte

dc, 28 bytes
97[ddPAP1+2z8*B-^+z27>M]dsMx

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Outputs to stdout, makes lowercase letters
Explanation
P pops a number from the stack and outputs it as a base-256 byte stream. So I use some math to calculate each number (representing the appropriate string) "inductively" from the previous.
97        A literal, which P will print as ASCII 97 ('a')
[         Each loop starts with these two things true:
              The next number to Print is on top of the stack
              The stack depth is the # of times the loop has started (inclusive)
  dd        Make two copies: one to manipulate stack depth, one to print
  PAP       Print the number, then Print a newline (0x0A)
  1+        Increment the last digit (i.e., the letter)
  2z8*B-^+  Add the leftmost space, calculated as:
                 32*(256^loop counter)  (because 32 = ' ')
               = 2^5*(2^8)^(z-2)        (z = stack depth = counter + 2)
               = 2^(8z-11)              (and to dc, 'B' pushes literal 11)
  z27>M     Repeat unless this was our 26th time through
]dsMx       End the loop, store it as a macro, and run it

Red, 37 bytes
repeat n 26[print pad/left #"`"+ n n]

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Dart, 65 bytes
f()=>List.generate(26,(i)=>String.fromCharCode(i+65).padLeft(i));

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MBASIC, 43 bytes
1 FOR I=0 TO 25:PRINT SPC(I)CHR$(97+I):NEXT

similar to Alphabet Staircase.

Python 3 43 Bytes
for i in range(26):print(" "*i+chr(i+97))

Pushy, 10 bytes
`a\0x1A;`:"32}h

Where \0x1A is the character 26, 'SUB'
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Rockstar, 55 bytes
X's0
while X-26
cast X+97 into C
say " "*X+C
build X up

Try it here (Code will need to be pasted in)

Husk, 9 bytes
z:¡Θø…"az

Try it online! ¡Θø is the infinite list [""," ","  ","   ",...], and …"az is the lowercase alphabet.

Deadfish~, 827 bytes
{{i}}dddc{{d}i}iiic{ii}iic{iiiiii}iiiiiic{{d}i}iic{ii}iicc{{i}ddd}dddc{{d}i}ic{ii}iiccc{{i}ddd}ddc{{d}i}c{ii}iicccc{{i}ddd}dc{{d}i}dc{ii}iiccccc{{i}ddd}c{{d}i}ddc{ii}iicccccc{{i}ddd}ic{{d}i}dddc{ii}iiccccccc{{i}ddd}iic{{d}i}ddddc{ii}iicccccccc{{i}ddd}iiic{{d}i}dddddc{ii}iiccccccccc{{i}ddd}iiiic{{d}i}ddddddc{ii}ii{c}{{i}ddd}iiiiic{{d}}iiic{ii}ii{c}c{{i}ddd}iiiiiic{{d}}iic{ii}ii{c}cc{{i}dd}dddc{{d}}ic{ii}ii{c}ccc{{i}dd}ddc{{d}}c{ii}ii{c}cccc{{i}dd}dc{{d}}dc{ii}ii{c}ccccc{{i}dd}c{{d}}ddc{ii}ii{c}cccccc{{i}dd}ic{{d}}dddc{ii}ii{c}ccccccc{{i}dd}iic{{d}}ddddc{ii}ii{c}cccccccc{{i}dd}iiic{{d}}dddddc{ii}ii{c}ccccccccc{{i}dd}iiiic{{d}}ddddddc{ii}ii{cc}{{i}dd}iiiiic{{d}}{d}iiic{ii}ii{cc}c{{i}dd}iiiiiic{{d}}{d}iic{ii}ii{cc}cc{{i}d}dddc{{d}}{d}ic{ii}ii{cc}ccc{{i}d}ddc{{d}}{d}c{ii}ii{cc}cccc{{i}d}dc{{d}}{d}dc{ii}ii{cc}ccccc{{i}d}c

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Julia 1.0, 31 bytes
@.println(" "^(0:25)*('a':'z'))

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Elixir, 51 bytes
Enum.reduce ?a..?z,"",&(IO.puts([&2,&1])&&"#{&2} ")

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Thunno d, \$ 12 \log_{256}(96) \approx \$ 9.88 bytes
AzA{s' *s+ZK

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Explanation
Az            # Lowercase Alphabet
  A{          # Enumerated for-loop:
    s         #  Swap so the index is on top
     ' *      #  Multiply " " by the index
        s+    #  Swap and add the character
          ZK  #  Print with a trailing newline
              # d flag stops implicit print at the end

Thunno N, \$ 12 \log_{256}(96) \approx \$ 9.88 bytes
Az26R' *ZZ.J

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Explanation
Az            # Lowercase Alphabet
  26R         # range(26)
     ' *      # Multiply " " by each number
        ZZ    # Zip together
          .J  # Join each inner list
              # N flag joins by newlines
              # Implicit output

Uiua 0.3.1, 17 bytes
+@ +×65⊃∘×⊞=..⇡26

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Python 3, 51 bytes
lambda:"\n".join(" "*i+chr(i+97)for i in range(26))

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Wait, why do you need lambda if you can print it with same count of bytes?

hang on im going to try to golf it a bit

Swift, 89 86 bytes
zip(0...,"abcdefghijklmnopqrstuvwxyz").map{print({String.init}()(" ",$0.0)+"\($0.1)")}

all_licenses: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/3.0/

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