Lots of good suggestions in this thread, just let me add a few that weren’t mentioned yet:
Lord of the Ice Garden is a game after a polish scifi/fantasy book, where players play scientists gone mad that try to take over (each one on his own) a magical world while being hunted by some guy from back home who wants to stop them and bring them to justice. It is an interesting mix of area control, worker placement with lots of other mechanics thrown in. Slightly fiddly on the first plays but strangely addicting. Aside from setup variance there is no luck whatsoever in the game, it boils down to pure strategy, which can crank it up on the “brain burner” scale quite a bit sometimes. Each player has a very distinct win condition and a pool of units they can use with very different abilities. Sadly I haven’t brought it to the table multiplayer, yet, only played it solo. It is a beast to teach.
Wir sind das Volk is a very interesting historic game where one player plays West Germany and the other East Germany, duking it out ideologically and economically over 4 decades. Both countries play very different, West Germany is trying to run down the economy or ideology of East Germany, while the East is just trying to hold on to a crumbling country, fighting fires all over the place, trying to survive (and especially survive the end-of-decade phase that consists only of bad things happen to the east). In this one, both players really play two different games that just happen to be on the same board, interacting heavily with the other side.
Then there are the COIN games, which are on the border of war games and euro games (for me they feel quite euro-ish, so right up my alley). I am currently playing Cuba Libre, where you play the different factions in the cuban revolution (Batista regime, Castros guys, the Directorio and the casino syndicates), each with it’s own win condition and very different strategies and abilities. The whole game is driven along by a series of cards representing different historical events or people and you try to get your guys into a position where they can hold up against the opponents. Fun thing is that you allways play 4 factions, but those that are not run by a player are run by bots. That game jumped up to my top games immediately and I totally look forward to upcoming titles I have on preorder (one for the american revolution and one for the gallic wars). There are some others about the vietnam war, the colombian guerillas and Afghanistan. For a history-buff like me it’s pure gold 🙂
Hannibal: Rome vs Carthage and Polis: Fight for the Hegemony are two other historically based games. Polis is interesting in that the differences of players are actually very small – it’s mostly the starting setup and availability of ressources, and the (at first sight) little difference of who strikes first in battles on land (Sparta) or ocean (Athens). But those little differences actually play out very differently during the game. Hannibal on the other hand has bigger differences in players, with regards to troups and available generals and the way they play out. Both games again are driven along by some event cards, where Polis only provides small triggers each age but with Hannibal the cards really push the game along.
And one that comes to mind is Sentinels of the Multiverse, where each hero plays very differently due to his/her deck of cards, often pushing them into really different directions (healer, tank, attacker, deck-manipulator). And many coop or 1-vs-many games can provide very different hero setups, too.
