My top two-player games aren't necessarily designed solely for two players. In fact, a game being strictly designed for two players is often a deterrent to me because I often game with at least more than one other friend—or at least want the flexibility to do so. That being said, unlike Firestone, my wife is a closeted gamer at heart. While she will deny it in public, she has, over the last 10 years of our marriage, ventured pretty far down the dork path from time to time. So it's not uncommon for a fly on the wall to see us sitting at the dining room table in heated competition. My only complaint in all of this is that she's a pretty bad cheater (again, something that she denies implicitly), and while I have no grounds or basis for such an accusation, I firmly believe foul play is afoot when she and I game.
Anyway, enough about my suspicions, here's a quick list (in no particular order) of some great games for two players.
While this game is designed and published for two players, it's expandable for three to four players by purchasing a second core set. But for a real challenge go on a quest with only a single companion. This game will test your deck-building skills, as well as your strategic ability. I do often play with three to four players, and it scales well for the added players, but I love the challenge of the two-player game. Overall this has become one of my favorite games, and the LCG has become (to me) the perfect mix of CCG deck building, board game strategy and role playing story and plot development. If you're not playing this game, you should be!
Battlefield General: Spearpoint 1943
Collins Epic Wargames released this at Origins a few years ago, and a friend of mine grabbed it up. It's a really fun WWII-based deckbuilder; they've released some expansions since then and I hear the game keeps getting better. I'd like to play this more often, so I'll probably invest in my own copy pretty soon!
I know what you're thinking... Two-player Carcassonne? Trust me, the style of play is vastly different from a multi-player game. My wife and I play this one-on-one all the time; about mid-way through the game it becomes a very competitive battle for farm land. The cool thing is that the crazy strategy that requires eight perfect tile pulls to make happen can ACTUALLY happen! Just remember that when you're playing with more players, they generally don't work, unless of course you convince the other players to play tiles that help by assuring them it's the right move for their strategy... Not that I would ever do such a thing.
I totally prefer to keep the expansion in the game and play 5 players on this one. That being said, there is again a nuance to playing a two player game of Kingdom builder: Do you stay out of each other's way, and hope that you play the right scoring options to out-race your opponent? Or do you intentionally start some trouble and try to block out the other player from getting the nifty ability tokens?
Two players clashing for control of Greece by drafting creatures, soldiers, and the like, you war over control of three battlefields. A really slick game for two players that's quick to learn, and a lot of fun.