Well from my infrequent trips down there, I don't think there is a bar that hosts a "regular" wet underwear contest, but I think that Bourbon Street Bar has these kind of contests occasionally, usually hooked up to a holiday weekend or special event. However, they usually have 3 huge slabs of beef dancing on the bar every night and the only competetion would be how many dollars can fit inside their underwear.

If you walk diagonally across the street to the Saloon 1 on a Friday night at midnight they have a wet underwear contest without the underwear. Usually starts at 1am, as it takes people a while to get liquored up enough to sign up.

Of course, you could go to KWEST across the street and the boys dancing on the bar have dry underwear and usually will lose them for a buck.

This website usually has all the info for the bars...

http://www.pistolandenema.com/