These are all great Perl solutions, but you can also just do

md5sum * | sort
[download]

and let your eye pick out the pairs of MD5 sums that are identical.

As already noted, if you have a slow machine, and/or gigantic files, the MD5 process may take a while. My very simple test looked at about a dozen text files (tab-delimited tables) that were an average of 10K each in size, and that all took 24 msec. On a set of larger files (90M in total), it still only took 1.7 seconds. Sometimes simple is the best -- it depends on your situation.