I love strategy games, annd I absolutely love strategy games where there are multiple factions, each with their own win conditions. To me, this adds an entire metalayer to the game, full of Xanatos Gambits.
The best non-computer examples I can think of are the Dune board game from Avalon Hill, and the Steve Jackson Illuminati card game/CCG. For example, in the Dune board game, the Bene Gesserit, before the start of the game, write down another faction and a turn number. If that player wins on that turn, then they reveal this info and they win instead. Which is sheer awesome.
Or in the Illuminati card game, where everyone's actual faction identity (and thus, win condition) is secret. Which leads to fiendishly convoluted strategies, such as imitating the Gnomes of Zurich by accumulating high-income cards, which your opponents feverishly work to kill off, only to finally reveal that all the time you were the Servants of Cthulhu (who win the game by having a certain number of cards destroyed).
Seems to be a very popular mechanic in board games and card games, but rarely implemented in computer games. The Civilization games sort of have that in that one player could be going for a conquest victory, another for a cultural victory, another for a spaceship victory, etc. but it's not quite the same because the victory condition is still up to the player rather than dictated or enabled by the choice of civ.
Anybody else know some computer games with this sort of play mechanic in them?