How can I find repeated letters with a Perl regex?

Use \N to refer to previous groups:

/(\w)\1+/g

I think you actually want this rather than the "\w" as that includes numbers and the underscore.

([a-zA-Z])\1+

Ok, ok, I can take a hint Leon. Use this for the unicode-world or for posix stuff.

([[:alpha:]])\1+

I Think using a backreference would work:

(\w)\1+

\w is basically [a-zA-Z_0-9] so if you only want to match letters between A and Z (case insensitively), use [a-zA-Z] instead.

(EDIT: or, like Tanktalus mentioned in his comment (and as others have answered as well), [[:alpha:]], which is locale-sensitive)

You can find any letter, then use \1 to find that same letter a second time (or more). If you only need to know the letter, then $1 will contain it. Otherwise you can concatenate the second match onto the first.

my $str = "Foooooobar";

$str =~ /(\w)(\1+)/;

print $1;
# prints 'o'
print $1 . $2;
# prints 'oooooo'