I'm a relatively inexperienced gamer, so I know of only a few. However, among those I've found interesting include, but are not limited to:
1. GLaDOS - essentially the HAL 9000 computer reborn. Sits somewhere between kind and terrifyingly cruel, but somehow comes off as witty in the process. Also a suprisingly good vocalist.
2. Gordon Freeman - what makes this character intriguing is that he isn't really a character; he never speaks, he doesn't vent personality or spout catch phrases, he doesn't have signature moves. Your imagination fills in the blank, and being that HL2's design is absolutely remarkable, with combat being approachable in ways I haven't seen in games since (anyone remember the gravity gun), you adapt to your own personal favorite styles (and what your PC can handle if you're on an ancient machine). Gordon is you.
3. Solid Snake - supersoldier with genetically enhanced aging called in to turn the tides of war, destroy weapons of mass destruction, and still keep his cool while fighting enemies with ridiculous names (dirty duck?) and piloting mechs (REX is awesome). He seems cold, harsh, and on point.
4. Andrew Ryan - I don't think anybody will ever look at the words "would you kindly" the same again.
Do note that these are characters who are your "favorite", but characters with an interesting psychological profile. It's like comparing Rorschach to Captain America - both make for a fantastic story if handled correctly, but Rorschach has depth, while Captain America comes off a bit more like a tool, but that's just me. Yeah, so I would be most suprised to find the likes of Nathan Drake or Master Chief or Kratos on this list. Isaac Clark is a possibility though. I wouldn't vouch for Marcus Fenix though - he seems like the 360 equivalent of Kratos: massive, muscular, yells a lot, is one of the leading figures on his console, his game bears the title G____ of War, and is often times seen battling either massive or plentiful creatures among blood stains and strewn limbs.
[Insert witty afterthought here]