Comment Depth Limit for Fish (Score 5, Informative) 33
A recent article in New Scientist (paywalled, I don't have an alternative) suggests that 8 km is about the limit for fish. The problem, apparently, is that the pressure distorts protein shapes, eventually preventing them from working properly. The tissue (particularly muscle) of deep-sea fishes contains trimethylamine oxide, which may protect against this problem, and the deeper you go, the more of it the fish have, but by about 8km they are saturated with it.
Invertebrates have been found deeper, so presumably they have a different mechanism.