Well... my experiences differ a little bit from everyone else's. Granted that I've always sucked at fish, I have managed to keep quite a few types long-term, and very few wrasses have managed to earn a spot on that list. I have killed many, many wrasses.
Yes, sixlines and mysteries and their relatives with similar body-shapes are evil. Please avoid.
Fairy wrasses:
Many (maybe even the majority?) of these guys do best in tanks with too many fish where you've got piles of other active swimmers to keep them busy. They seem to thriiiive in these situations, see: http://www.youtube.com/user/SDreefguy#p/a/f/0/5_oR0WfjQrE.
In a 'typical' reef with a tang or two, a couple clownfish, and another few fish, they seem to find some excuse to just wind down and disappear after a year or two. Most of the species that manage to hit the 2yr mark in a mellowish reef such as yellowfins (first hand exp), and scotts (second hand exp) are a bit bastardly themselves.
Cryptic wrasses:
Possum wrasses and similar seem to live long term. But you'll rarely see them.
Halichoeres wrasses:
Yellows and radiants are great fish, they eat bad bugs, they're colorful, they swim around, they're awesome. The radiants seem a little bit flimsier than the yellows (just more shipping stress?) but even still, I count on having to replace the yellows around the 2yr mark. Coris pictoides behaves somewhat similar to these guys, gets to a similar size, and gets a spot on the long-term list... buuut they're also slightly more aggressive.
Leopards:
At least for the bipartitus - if you don't have other fish that chase them to death... once you get them eating, they're rock solid.
Anampses and anything that swims like a freakin spastic pingpong ball:
Just don't do it. They're too unpleasant to watch even IF you're a fishkeeping prodigy and manage to keep em alive for the long haul.
