At the moment I only have a laptop and a PS2 to play games on, so all my games are old =D
Fallout: New Vegas is really perennial with me. It's the game I find I can just keep on replaying, my strategy nowadays is to go to the F:NW wiki and then roll dice or something to select a random faction and a random three 'tagged' skills. Then I try to figure out what sort of person might have those characteristics and play that character.
For example on my last playthrough I had Ceasar's Legion with Science, Medicine and Energy Weapons as my tagged skills (also I almost always play women). I figured that my character had a complete lack of empathy for other people, but admired those who found the strength to dominate others. The Legion's hatred of Science, Medecine and Energy Weapons didn't bother her, because she saw those as tricks to keep the peons in control. And her ego didn't let her see herself as a peon, instead she was a powerful ally that Caesar would want to do business with, and of course those restrictions didn't apply to her. (The story totally let me do this too. I arrived at Caesar's camp and he actually basically straight up described me as that kind of person).
Final Fantasy X and Dreamfall: The Longest Journey are the big ones for me atm.