Thread title sums it up. I'm thinking of games like Dominions3, Sword of the Stars, Neptunes Pride, etc. Games that work well multi-player and require player interaction beyond just attacking everybody.
The one area (IMO) all the above games falls short is diplomacy. Although you can create alliances in the game, at the end of the day, there can only be one winner, so they all encourage a backstabbing mentality. Which is fine for something like Solium Infernum, it fits the theme perfectly. But for some of the other games, I wish they would allow for non-zero sum trading and alliances, so we get richer dynamics.