The Night's Watch is a service of men—and only men—who protect the realm from wildling raiding parties. In A Clash of Kings, the Night's Watch has entered the lands beyond the Wall on the Great Ranging to find out what's become of Benjen Stark and also why those dead people keep coming back to life as ice zombies. That second part, in particular, seems like something one should know the answer to, right?
Mormont is the leader of the Night's Watch and Jon Snow's mentor. A total pragmatist, Mormont sticks to his goal of defending the Seven Kingdoms even if this means working with men as unsavory as Craster (24.Jon.196). Mormont personally leads the Great Ranging. Despite being much older, he refuses to show weakness to the younger men under his command (35.Jon.6), and he is last seen setting up defenses at the Fist of the First Men.
Sam is Jon Snow's best friend and also a pretty intelligent fellow. He joins the Great Ranging as the Commander's aide, caring for the messenger ravens, writing letters, and crafting maps. Despite being a self-proclaimed coward, Sam seems to have found a bit of his courage on the journey north, which is really saying something in a frozen land where everything and everybody wants to kill him (14.Jon.43).
Qhorin is a ranger in the Night's Watch. He leads a scouting party to try to discover what Mance Rayder is looking for at the Frostfangs, and is joined by Jon Snow. En route, Qhorin teaches Jon lessons about how to lead men (54.Jon.29). Eventually, the scouting party is discovered by Mance's patrol, and although Qhorin tries several tricks, the wildlings eventually corner Jon Snow and him. Qhorin attacks Jon and allows himself to be killed, making it seem that Jon Snow is a traitor so that he may join the wildlings as a double agent (69.Jon.102)
The three other Night's Watchmen who join Qhorin Halfhand's scouting party. Although all three are supremely talented bros in black, they are all killed during the return trip to the Fist of the First Men.
Alliser sure is a prickly member of the Night's Watch. He travels to King's Landing to warn the king about the threat of the Others and to recruit reinforcements, but unfortunately, his proof—a still moving hand taken from one of the Others—disintegrates in its jar before he can have an audience.
These two brothers of the Night's Watch have no love lost for Jon Snow and try to pick a fight with him at Craster's Keep. Jon overhears them having a mutinous-sounding discussion on the Fist of the First Men, but he writes it off as nerves and fear.
Dolorous is a sullen, pessimistic guy. Seriously, nothing can cheer him up. He's basically the C-3PO of the Night's Watch.