These are the games my group has been playing during the past month:
Diplomacy: this game is just so much fun and interesting but we often hesitate to play it because of the social mechanics. In diplomacy being stabbed in the back is worse than in any other game I've played because every single game-state update is incredibly meaningful. In this game emotion often drives decision-making, leading to very memorable situations. We've played it with 4 players (one didn't want to play it because she tends to take things personally) and then continued via WhatsApp and e-mail.
Battlestar Galactica + expansions: one of the all-time favorites of my group. Highly thematic, replicates the sense of urgency from the tv series well and also has very interesting social dynamics. We've played it around 12 times before the human side found itself playing using the exact same strategy repeatedly and winning almost every single time, hence we removed some of the cards that supported this strategy and kept things interesting for both sides. The one drawback of BSG is that one person is bound to come up with a 'masterplan' and whoever doesn't cooperate gets labelled a Cylon because he's not doing what's obviously best for the group.
Flash Point: Fire Rescue: easy to learn game and well balanced. Tactical rather than strategical (which prevents a player from ordering people around like in BSG), sufficient meaningful choices during a turn and interesting AI (fire-spreading). If we want to play a cooperative game within one and a half hours it's usually Flash Point. It scales really well with different numbers of players and within two turns even newcomers can get into it and due to the AI's randomness the game doesn't become a puzzle.
Gears of War: The Board Game: the surprise game of last month. It's a 1 to 4 player cooperative dungeon crawler without the need for a DM (AI cards take care of ordering enemies around). It plays somewhat like a board-game version of XCOM but with mechanics lent from the GoW series and the scenarios replicate some of the video game series' setpieces. Chance does play quite a big role in attacking and defending but the use of order-cards give players sufficient meaningful choices, Because of the automated but still fairly unpredictable AI (which works quite well) the game revolves around short term tactics more than long term strategy, which in my group is a good thing. Oh, there's also Horde Mode in multiple difficulty levels.
Puerto Rico: still a classic in my group and the eurogame of choice. We do see players doing the same opening moves over and over, going for the same type of buildings they always go for, but the randomization in resources forces players to adapt their strategies keeping the game interesting every time. Personally I feel the game is always over a little too soon but maybe I'm just using long-term strategies too often. Nevertheless, Puerto Rico is the game that gets played most in my house, partly because it doesn't take too long to set up and play.
Race for the Galaxy: basically a card-game version of Puero Rico with a different theme. We prefer Puerto Rico because with RFTG bad luck with drawing cards often undermines strategic play, for example, not drawing any military worlds if you went for that strategy (your starting planet might encourage you to use military strategy). I also think that with RFTG there is less opportunity to influence other players' decisions. But on the other hand, once you've played a couple of times and know which cards are in the deck the game gets more interesting again, and because it's so short it's my vacation-eurogame of choice.
I have Arkham Horror and Twilight Struggle on the shelf, unplayed. We expect AH to be our next big coop game, cooperative (thematically rich) gameplay is our favorite and in general we prefer long games over short ones. Therefore I'm confident my group will like it. I also really want to buy Twilight Imperium some time but I've got so many hours left in all these games that I'm holding out until we really want to play something new again.