I could talk about this a lot, because I really like the civ genre of games, but I feel like I still haven't found the "perfect" game. That's not even taking the challenge of "Does it work with 2P?" into account, lol
I'll comment on some of the different games I've played, though:
Sid Meier's Civilization: The Board Game - I like that this game has different types of victories to go for; and it's possible to avoid war. Many of the things from the computer game are represented here. Unlike a lot of civ games, "Culture" has a little more weight to it, because you gain abilities from it, it's not just a meaningless number. However, there are a million pieces to this game, and it feels like too much. Plays pretty well with 2.
Through the Ages - I like this game; it feels very well-designed. I like that you have two central resource pieces (Population, and Resources), but many options for how to assign them. This very elegant central mechanism makes it feel pretty unique from computer Civ games. Unfortunately, the theming and sense of "wonder" that you're "building something" comes through rather dimly here, since it's rather abstract. It plays very well with 2, though.
speaking of wonders
7 Wonders - This game is supposed to be bad with 2P, but reportedly a 2P version is coming out soon. I loved this game when I first played it, but Science being the only apparent strategy to the game kinda killed it. However, it's a short, simple, and sweet Civ game. Some say it's not a civ game, but I think it hits the spot better than "Nations the Dice Game".
Nations the Dice Game - I played this game once, and it was about as dry as a game can get. Eh.
Patchistory - Really interesting, unique take on a civ game from Korea. With cards, you create a growing 'quilt' of resources, infrastructure, leaders, and wonders that become your civ. You certainly haven't played this on a PC. It's a good collection of ideas, but lacks some optimization, though. It almost works with 2, but the auction phases in any game for 2 players are dull. A good variant for that phase of the game would make this awesome for 2P.
Polis: Fight for the Hegemony - Although this looks (and sounds like) a war game, this is a very good civ game specifically for 2. The game is extremely tense and difficult, even if you never battle, as a lot of it is an economic and resource game. I really like that you take control of cities, and then try to cultivate them by growing the city populations (people cubes that can either stay in your cities, or go out onto the board as trained units), and building different works in your cities. The point of the game is not to fight, but to have the biggest population.
Struggle for Catan - It's a card game with a lot of the Catan logic, but it's quite a different and unique game, and specifically made for 2. Though perhaps not the "big picture" you want from a civ game. I like that you are zoomed in a little closer to the Catan world, building individual buildings that will give you certain benefits, while also fighting off different hordes. The different expansions for this game are pretty interesting, as they all change the style of game quite a bit.
That's all I can think of for now, more to come
