Old Ways Are Best!
Mature gamer (teeth cut on the AH classics), so I think of myself as a war gamer primarily but appreciate what the Euros have done for the hobby.
I gravitate toward empire building strategy games. However, our group prefers games that take about four or five hours at the very most so some of the heavier types don't get a lot of play. Civilization, Age of Renaissance and Twlight Imperium are reserved for the infrequent "all-day" affairs we can occasionally fit into a long weekend. What a wonderful find Eclipse has been for us as the near perfect Civ style game that plays comfortably in our sessions - sometimes twice with only three or four players!
Right now, Britannia is on the outer edge of fitting the bill as much as I enjoy it. Revolution: The Dutch Revolt, 1830 and Die Macher are on the bubble as well, which is a pity since those games are great!
I've found that a lot of Martin Wallace's designs hit my "sweet spot" these days. I will play most of them without hesitation: Brass, Rise of Empires, Struggle of Empires, Steam, Princes of the Renaissance - the list goes on and on. I also greatly enjoy many of the card-driven strategy games (CDG), but some of them also push the time envelope.
I don't get the opportunity to play many two-player games anymore, but when I do Hannibal: Rome vs. Carthage, Twilight Struggle, War of the Ring and A Few Acres Of Snow are among my favorites. I have to figure a way of squeezing more hours into a day!