Shadows Over Camelot is primarily a cooperative game in which the players are working together to get enough "white swords" before too many "black swords" are earned. Both of the types of swords are collected from quests - successful completion of quests will earn white swords, whereas failure in a quest will increase the number of black swords. With that said, on a typical player's turn, they must choose which evil action occurs (this is how the game plays against you), and then they make a "Heroic action". The evil actions, as I'm sure you guessed, work towards you failing different quests, and thus enhance the chances of you getting black swords, whereas the Heroic actions are ways in which your knight is able to work quests towards successful completion. Some of the Heroic actions that can be taken include moving to a quest, playing cards towards a quest, playing special cards, healing, and (if playing with a potential traitor) accusing another knight of being a traitor.
Shadows Over Camelot is an incredibly well balanced game. There are several different quests that are all going on at the same time, and it is up to you as the knights of the round table to make sure that you don't ignore any of them for too long, or else you will fail them and start getting negative victory points (black swords) very quickly. Also, some of the quests are harder than others, but many of the quests that are more challenging are also more rewarding - you may discover Lancelot's armor or the Holy Grail.
Another good thing that Shadows Over Camelot introduces is the potential of their being a traitor (this is an optional way to play). Whereas in Pandemic you know that nobody will betray you and in Battlestar Galactica it's just a matter of time, in Shadows Over Camelot you have to deal with the possibility. And if you start accusing people wrongly of being a traitor you will 1) turn your white swords into black swords and 2) probably have people start accusing you (thus causing another sword to flip over).
Another factor of Shadows Over Camelot that adds to its replayability is the different knights involved. Each of the knights has a special power (similar to a role in Pandemic), which allows them to help your team in a unique way - whether that might be by moving to a quest for free, drawing cards, giving cards to other players, or something else. This element of the game allows you to play differently many times through, and especially if playing with the potential of a traitor, it is interesting to see how a traitor tries to use his special power in negative or useless ways without getting caught. (As a note, if you do ever play the game out, there is an expansion - Merlin's Company - that allows you to get some more plays out of your game.)
One final interesting aspect of the game is that your knights can die. If you fail enough quests, your knight's life will eventually expire, thus causing you to be eliminated from the game. In fact, one of the ways that the traitor can win is by letting all of his fellow knights be killed off.
Overall, I give Shadows Over Camelot a 9.0/10. The more I think about this game, the more I think that it is on the same level as Pandemic when it comes to cooperative games, and so I felt it was only fitting to give them the same score. However, whereas Pandemic is for 2-4 players, Shadows works very well with a larger group, and can be played with 3-7 (and works best with lots of players when using the traitor).
In addition to Shadows Over Camelot, you might also check out Cargo Noir, Castle Panic, and Mystery Express.