It is rare that I play a cooperative game and like it a lot. Most of them either feature extreme luck and randomness or have the '1 player problem' where the best player plays everybody's turns for them. I can certainly see how either sort of game would be fine for a group that isn't especially competitive - just do whatever you want and win or lose. I find the trick is figuring out a cooperative game where there exists a lot of strategy and challenge while preventing 1 player from running the whole show; information needs to be kept hidden to a substantial extent.
Pandemic is an example of a game that doesn't manage this very well. As written 1 player can know everything and make all the decisions so each person often feels like they have nothing to contribute. It is easy to change that by keeping all cards held secret but the game ends up feeling less fun when players cannot talk about strategy at all. A big part of the appeal of a coop game is discussing strategy and trying to convince the other players to run with my crazy plan!
I have recently been playing a lot of Sentinels of the Multiverse and it seems to me to be the best designed coop game I have found. Thematically it is a battle between the players, each of whom represents one of the ten possible superheroes, against one of the four possible supervillains. To keep things more unique there are four environments in which the battle can be fought like Megalopolis, Wagner Mars Base, Atlantis, and a dinosaur island. The thing that makes this excellent mechanically is that each hero has cards that can be played and Powers that can be used; one card per turn and one Power per turn. Because of this players can discuss use of their Powers and general strategy while keeping their cards secret. It gives a nice mix of strategy "I will blast the dorks, you deal with the erupting volcano" but with significant information being secret one player cannot reasonably play the whole table.
One very valid criticism of SotM is that the balance of many things is way off. You can see four heroes in the image above, two of which are excellent and two of which are rubbish. While Tachyon and Legacy (in white) aren't twice as good as Absolute Zero and Bunker they are at least 50% better and that makes something of a mockery of balance. On the other hand the game can be played with 2-6 players and the villains scale very poorly with the number of players so you can always just play with crappy heroes if you have a lot of players and good heroes if you are shorthanded. The villains and environments themselves are also pretty variable in terms of power so it is possible to arrange anything from a trivial victory (6 players vs. Omnitron using best heroes on dinosaur island) to a nearly impossible situation (Bunker and Absolute Zero vs. Citizen Dawn on Wagner Mars Base).
One thing I wish they had done is include a sensible power rating for the various heroes and environments. The villains have reasonable difficulty ratings but it would have been nice to not have to play the game a lot to figure out which challenges were going to be impossible and which would be trivial. Either way though the game is a hell of a lot of fun and I recommend it highly. Elli has been enjoying playing with us at age 6 although she needs a lot of help but there are often really interesting strategy decisions for advanced players. The game has a great combination of fun and variable challenge that I approve of heartily.
picture from: http://sentinelsofthemultiverse.com/