Hmmn…
A few favourites, divided into light (casual gamers) and heavy (proper geeks).
RPG: light, It Came From the Late, Late, Late Show (b-movie comedy RPG. Bad monster attacking? Call in your stunt double…). Heavy, GURPS (comprehensive system that can handle almost anything, but requires an experienced GM).
Wargame: light, Small World (cheesy, fun, simple). Heavy (but not that heavy), Sails of Glory (gorgeous miniatures and simple rules, but a bit fiddly and requires a decent sized table).
Abstract tactical: light, Tsuro (fast and fun, enough luck involved that novices have a decent chance). Heavy, Khet (very simple rules, but chess-like depth; an experienced player will slaughter a novice).
Co-op: light, Forbidden Island. Heavy, Pandemic (these are basically two versions of the same game, but the first is faster, simplified, and has a more kid-friendly theme).