Already got some good recommendations here. Though, start at the beginning if you're planning on going with Mass Effect - the first game might be starting to look a little dated by now, but the story was intended to take place over a trilogy of games from the beginning.
Fallout is worth a look, too - personally, I prefer New Vegas to 3, though, but that's just me. They're both good. New Vegas seems to me like it has more replay value, too.
Elder Scrolls: Oblivion is an option, as well, although that's going back a few years now. Skyrim will be out soon, too.
Deus Ex: Human Revolution will be out pretty soon, and so far I've neard nothing but good things about it.
Also, Bioshock, maybe. Or, Red Dead Redemption. Grand Theft Auto 4. And, there's a decent collection of entertaining games on download from the live arcade.