Co-op (or cooperative) games can now be found in abundance. There's something fresh about playing with the people sitting next to you instead of against them. In co-op games, the game itself (and sometimes a traitor) is the opposition. These games, accordingly, tend to be hard-to-beat, with a "let's play one more" when victory slips away at the last moment.
This isn't a complete list by any means, but it does give some of the breadth of the genre. They're not ranked in any particular order, either. These are all good games, and cover the range from quick, casual games to invested endeavors.
Pandemic: Perhaps because it was the first one I played, this sticks in my mind as the classic co-op, enjoyed by casual and dedicated gamers alike. Many co-ops have roles for each player with special abilities, but in Pandemic, you always hurt for the missing roles. Everyone works together to try to stop outbreaks of relentless diseases from sweeping over the globe.
Shadows over Camelot: This game is longer than Forbidden Island, but the rules are similarly easy to grasp, based on cards numbering 1-5. It also plays a lot -- up to 7 -- making it great for a crowd. I've played it with all adults, but this would be an easy one to include a younger player with, too. This game includes the possibility of a traitor (a player secretly working against everyone else) which adds to the fun.
Anyone have a favorite co-op I left off the list?