Increment the depth until you get nothing back.

Update 1: Oops. I accidentally declared $depth twice.
Update 2: I accidentally put a semi-colon after `my depth = 0` which screws up the parameters for the for(;;). Replacing it with a comma keeps the correct meaning.

my @stack;
for ( my $depth = 0,
      my $frame = [ caller $depth ];
      scalar( @$frame );
      $depth++ ) {
    push @stack, $frame;
}
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I like that you have both the stack to inspect (eg. dump it to stderr) and the stack depth (scalar(@stack))

For my liking though, this is more intuitive:

my @stack;
my $depth = 0;
while (my @frame = caller $depth++) {
    push @stack, \@frame[0,1,2];
}
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The entire purpose of the for(;;) loop is to handle preinitializations and temporary variables like your my $depth = 0 and to separate your test scalar( @frame ) from your NEXT() in $depth++.

my $depth = 0;
$depth++ while caller($depth);
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Yes, this works fine. I tweaked it a bit, setting $depth to -1 and putting the code in a GetCallStackDepth sub. Cool!

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A fair fight is a sign of poor planning.

I tweaked it a bit, setting $depth to -1

Wouldn't your subroutine always return -1? Shouldn't your GetCallStackDepth look more like:

sub GetCallStackDepth {
  my $depth = 1; # 0 is this sub, why bother checking it?
  $depth++ while caller($depth);
  return $depth - 1;
}
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