Far cry 3 is Amazing, it's addictive FPS and has a great storyline. One of the best games I've ever played. I would seriously reccomend this game.
Portal 2 has a funny, interesting storyline and is sci fi style with puzzles. It's really enjoyable. I love Wheatley in it, he is awesome. :)
Modern warefare 2 is one of my favourite FPS, but there are many more, battlefield 3 is pretty good as well. The online gameplay is addictive.
If you like sandbox and zombies then Dead Rising is a fun game to play, you can kill zombies with dustbins, chainsaws and combine weapons to make some ludicrous stuff! Their are others games like this, a new one out is State Of Decay, which looks better than Dead Rising as it involves setting up outposts, driving cars and seems more realistic. (only played demo though).
Another great zombie game is The Walking Dead which has a great storyline, over time you end up really caring for the characters and the choices you make changes the storyline.
If you want an sinister small arcade game then check out Limbo, it's creepy and full of puzzles.
That's all I can think of for now.
Feel free to add me on Xbox live if you ever wanna play multiplayer on something, just message me and I'll get back to you.