FPS games and any games that revolve around guns and shooting have a few key gun types. Most of these guns appear in every FPS in some form, and they all have their uses (and abuses).
1. The Unlimited Gun: While not technically always a gun, there's usually some weapon that can always be used when you run out of ammo. In Wolfenstein it was the combat knife, in Republic Commando it was both the pistol and the knife/melee, and in Halo is was a melee strike. Of course, who can forget the devastating Impact Hammer of Unreal Tournament. These are last resort weapons, and a lifesaver when you are out of ammo.
2. The Rifle: The long range gun that remains accurate, but fires painfully slow compared to everything else. This gun has the largest variety, from various Sniper Rifles to the Shock Rifle of UT. Whether it's got a scope or not, this gun is designed to take out a target from a long range. It works best when the enemy doesn't know you've got him in your sights.
3. The SMG/Minigun: A tornado of bullets is the best way to describe the SMG/Minigun. Putting as many bullets in the air as possible, hoping that some hit the target, and scaring the enemy to death are the goals of these beautiful weapons. The aptly named minigun from UT, and Return to Castle Wolfenstein's Venom Gun are both beautiful examples of the suppressing fire of the minigun.
4. The rocket launcher/grenade launcher: Lots of enemies call for lots of explosives. Panzerfausts, Rocket Launchers, Brute Launchers all have one purpose: blow people up. The pinnacle of this weapon type is the UT rocket launcher, which can launch grenades as a secondary fire.
5. The BFG: The big one. It has severely limited ammo, and a grudge against anything that is alive. UT's pocket-nuke the Devastator and Return to Castle Wolfenstein's Tesla gun show this vengeance.