Well, for the main three characters, Sly's (middle guy) weapon is his cane, with is basically one of the most important items in the game, and the Theivius Racoonus (clever name right?). And Bentley's (the one on the right) is his crossbow and darts and bombs (he is mostly a techie, he doesn't fight much). And Murray's (the one on the left) is just his fists, he is really strong and can kill a guard in one punch. 
The rest of the characters are in the third game (except Carmelita). Carmelita's weapon is a plasma blast (Carmelita isn't a theif though, she's a fox cop, who sly happens to have a crush on, not in picture). Panda King (the giant panda dude) has a firework launcher. Penelope's (all the way right in bottom picture) (probably my favorite character in the game) weapons are RC vehicles, machines and a sword. The Guru's is his crystal ball (the purple dude in the bottom right).
