Obviously, Super Mario Bros. is a must, and it's a game that is timeless. I'd have to say they'd at least have to try a Grand Theft Auto game, not just because it's a well-crafted game, but especially for any casual gamer who's never really seen the game outside of the media hype.
The one series I haven't truly gotten truly into is Final Fantasy and I really should attempt a bit. I probably would have loved FFVII but unfortunately it's really hard to look at graphically now. I've played spinoffs (Tactics, FFIII on the DS), but haven't gotten truly into any of the newer ones. I think with FFXIII on the 360, I can officially dive into it.