But then you'd lose the original case information. You'd have to have a hash of arrays to preserve the different case variations.

Update:
Here's a way to do it with a hash of hashes: 
#!/usr/bin/perl 

use warnings;
use strict;

use Data::Dumper;

my @original_array = qw( THIS This That That ThAT ThAt ThAt THIS These
+ Those );
my %results;

map { $results{uc($_)}->{$_} = undef } @original_array;

print "Original\n", Dumper(@original_array), "\n";
print "Result\n", Dumper( %results ), "\n";

__END__
Original
$VAR1 = 'THIS';
$VAR2 = 'This';
$VAR3 = 'That';
$VAR4 = 'That';
$VAR5 = 'ThAT';
$VAR6 = 'ThAt';
$VAR7 = 'ThAt';
$VAR8 = 'THIS';
$VAR9 = 'These';
$VAR10 = 'Those';

Result
$VAR1 = 'THAT';
$VAR2 = {
          'ThAT' => undef,
          'ThAt' => undef,
          'That' => undef
        };
$VAR3 = 'THIS';
$VAR4 = {
          'THIS' => undef,
          'This' => undef
        };
$VAR5 = 'THOSE';
$VAR6 = {
          'Those' => undef
        };
$VAR7 = 'THESE';
$VAR8 = {
          'These' => undef
        };

[download]

In reply to Re^3: (almost) Unique elements of an array by Transient
in thread (almost) Unique elements of an array by Anonymous Monk

Title:
Use:  <p> text here (a paragraph) </p>
and:  <code> code here </code>
to format your post, it's "PerlMonks-approved HTML":


  • Posts are HTML formatted. Put <p> </p> tags around your paragraphs. Put <code> </code> tags around your code and data!
  • Titles consisting of a single word are discouraged, and in most cases are disallowed outright.
  • Read Where should I post X? if you're not absolutely sure you're posting in the right place.
  • Please read these before you post! —
  • Posts may use any of the Perl Monks Approved HTML tags:
    a, abbr, b, big, blockquote, br, caption, center, col, colgroup, dd, del, details, div, dl, dt, em, font, h1, h2, h3, h4, h5, h6, hr, i, ins, li, ol, p, pre, readmore, small, span, spoiler, strike, strong, sub, summary, sup, table, tbody, td, tfoot, th, thead, tr, tt, u, ul, wbr
  • You may need to use entities for some characters, as follows. (Exception: Within code tags, you can put the characters literally.)
            For:     Use:
    & &amp;
    < &lt;
    > &gt;
    [ &#91;
    ] &#93;
  • Link using PerlMonks shortcuts! What shortcuts can I use for linking?
  • See Writeup Formatting Tips and other pages linked from there for more info.