1 Struggle of Empires
Often hard to find and very expensive, in this multiplayer wargame, players take on the role of colonial powers; it rewards strategic feints, connivance and careful planning. Its innovative system of alliances makes for vicious bidding wars, and the tiles allow for as many paths to victory as there are players. Every game feels exciting and dangerous, like grabbing a downed power line with your bare hands. I'd advise anyone who enjoys intense negotiation and area control games to buy this one while there are still copies floating around.
Wallenstein redux, with better graphic design and a trickier board. Another multiplayer wargame that requires delicate maneuvering and negotiation. The ingenious cube tower, which "remembers" outcomes of previous battles, means no one ever gets to whine about bad die rolls. We have a house rule that whenever you talk to your enemies, you have to try to sound like Toshiro Mifune in Seven Samurai.
3 Chaos in the Old World
Textbook example of asymmetrical player powers. Although I'm not a fan of the slightly cheesy Warhammer universe, this game makes evil even more fun than usual.
4 Age of Steam (or, more recently, just Steam)
In America, when we go to university, we emerge tens of thousands in debt, trying to grind our way back to profitability. This notoriously cruel train game is a little like that, except it only takes a couple of hours to learn from your mistakes. Make $2, and you feel like you've summitted Kilimanjaro. The number of expansions out there make this game a good value, too.
5 1960: The Making of the President
Any game that can hinge on a Richard Nixon's shaving acumen gets my vote. Faster, smoother, immeasurably more balanced than Cold War thriller Twilight Struggle.
6 Battlestar Galactica
Playing this game as a Cylon is one experience no enthusiast should go without. Only play this with practised and willing liars, though. I had misgivings about the mechanics after a few plays, but if you approach BSG as a primarily social game, you'll have a lot of fun.
7 Nexus Ops
Another out-of-print masterpiece; this one could've been turned into a movie franchise. Glowing aliens duke it out for control of mines on a modular hex board, with a catch - everyone's victory point conditions are secret. Takes ten minutes to learn and ninety to play.
8 Europe Engulfed
Ever play Axis & Allies? Like that, except for grown-ups with even more time on their hands. A serious WWII game from the famously upstanding company GMT.
In case you need a break from carnage and colonialism. The GIPF abstract games all benefit from high production values and deep play. This one's the simplest to learn, toughest to master and my favorite of the bunch.
10 Battle Line
You'll never go back to Lost Cities after this poker-like filler card game, also by GMT.