Lilith is a speedy SMG-user. She has the highest damage output in the game, and arguably the best defenses with her huge shield, shield regen, and lots of evasion abilities (Intuition, Phase Walk). If you like to run and gun, this is the best choice.
Roland is a great support class for co-op. He's neither the best damage dealer nor the best tank, but has a good mix of abilities that makes him average at a lot of things. His ammo regen and healing ability are crucial to co-op play.
Mordecai is the best long-range damage dealer, and his pet is pretty ridiculous if you go down that skill tree. He lacks any sort of utility or group benefit beyond damage and a rare class mod that increases the chance of finding rare items.
Brick is great in playthrough 1, ok in playthrough 2, and incredibly bad once you finish PT2. His signature ability loses power the later into the game you get, until it finally becomes pretty awful at level 50. In addition, his weapon specialization (Rockets) is probably the worst of the 4. He can however become a pretty damn good damage soaker if you dump a lot of points in the tank tree.