Syd - she can temporarily swap her consciousness with someone else by touching them. it also appears that when she switches back, her and the person she touches also switch physical locations (it only happened that once with David that i can remember so i don't totally get that one)

Ptonomy - he can inhabit and read other people's memories. he also has a photographic memory.

Oliver - appears to be a pretty powerful telepath. he's been in the astral plane for 20 years which seems like that would kill a normal person. i guess Melanie freezing him helped keep him going. he's got a good amount of control on the astral plane since he can create things (the ice cube he lives in, the glasses, the "shield" he created to protect David and Syd), though it seems he was losing his mind a bit from being in there so long.

dude who's name i can't remember who had some kind of telekinesis where he could fling things away (seemingly into oblivion).

The Eye - (i don't remember if he had a name) i really don't understand what his deal was or if he had any real power or not.

Cary/Kerry - probably the most interesting one. they appear to be two separate people inhabiting Cary's body simultaneously. she doesn't age when they merge. when they split, they can feel each other's pain. they also seem to be able to heal by merging.

David - an omega level mutant that can pretty much do anything it seems. control matter on a molecular level, warp reality, teleport, read minds, etc, etc. in the comics he has multiple personalities that each have a power, but they didn't really get into that in the show. it appears this is all him.