Pandemic!
There's also a nice game Thunderbirds which works in a similar way and is based on the TV show (you each control a different character with different abilities, and you're dealing with disasters and working towards a few bigger objectives). Lots of puzzling out the best use of everyone's actions.
Mysterium is good too - one person is the ghost of someone who's been killed who doesn't talk but uses dream cards (slightly surreal pictures with a few different things going on) to give clues to particular people, places and things - and then tries to get everyone else to guess which combination is how they died. Hard to explain unless you can see the cards, but lots of fun.
Just One is a good light game. Person A picks a word (which they don't see), and everyone else has to write one word that will help Person A guess. If two (or more) people write the same word, Person A doesn't get to see those ones (we often play as a four with friends over Skype and we have all written exactly the same word before!) But basically you're all trying to work together to get the best score.
There's other light games that you can play competitively (trying to get the most right), or you just keep going until people get bored and not keep score - Conception is good for that (a bit like Pictionary, except you're using pre-existing symbols on a board to give clues to objects, people, films, places etc)
Hope that helps. Love cooperative games (and competitive ones for that matter!)