Settlers of Catan
Settlers is frankly awesome and fun, if you haven't played it yet you owe yourself the chance to. Pick it up and next time your dm is missing, play Settlers instead of Billy-Bob's-Mega-Munchkin- Stand-In-Campaign. I like economic theme games so my runner up to settlers is Avalon Hill's Acquire, which can be quite intense at times. I also think Monopoly can have the same level of strategy, gamblins, and planning of the other games, but since most of us have been playing since we were 2 then we don't like it anymore...
I like Mage Knight, I appreciate being able to play mini's without having to paint all the damn things, and I think their rules are pretty elegant. Heroquest would be up there too. All things considered, Risk and A & A are pretty low on my list. Compared to things like squad leader, etc., they are less war games and more dice rolling contests......
I recently learned to play cribbage, which rocks.