How deep can life exist in the oceans?
Well, we know from the old Trieste expedition that even the Challenger Deep in the Marianas Trench holds life. (Pilots Piccard and Walsh thought they saw a flatfish, though most scientists think they misidentified a holothurian (sea cucumber).
See cool graphic here
How much life goes that deep, though? In other words, are deep dwellers rare or common?
Near the 10.9-km-deep Challenger Deep is the newly discovered Shinkai hydrothermal vent, the deepest such vent known so far. 5,680 meters down, a submersible (the Shinkai 6500) Japanese and American scientists found much more life than they expected, sea anenomes, long-armed crabs, white clams, snails, and comb jellies. They were not surprised to find life by this low-temp (non-volcanic) vent, but they were very surprised at the amount of biomass the area could support.
One thing we keep learning about the Earth: if life is at all possible in any location, life sets its foot (or pseudopod, or whatever.) Keep finding the new species!