Your fists.

Just like a real life, you can punch people, zombies, demons etc.

Flashlight.

Yes you can use it to see in the dark, and you can also bash people, zombies, demons etc with it.

Chainsaw.

Nice melee weapon... err I mean tool to cut down trees.

Pistol.

Your basic sidearm, can hold 12 rounds.

Shotgun.

It's a shotgun, 5 or 8 [to be confirmed] shells can be tucked away in one.

Machine gun.

Like a pistol, but is bigger and fires faster. Holds 60 rounds in the clip.

Chain gun.

Like a machine gun, but only with multiple barrels so you can fire even faster.

Plasma gun.

Like a machine gun, but fires plasma I guess, can hold 50 shots in the clip.

Grenades.

For when you want a little more boom in your doom.

Rocket launcher.

What game from id hasn't had one?  Erm, okay well Wolfy 3D, and Hovertank 3D and a few other really old ones, but come on classic id weapon.  Can do 5 shots without reloading.

Soul cube.

This is a new weapon for Doom 3.  Basically after you've killed 5 demons, the weapon is activated, you can then use it to instantly kill a demon, it transfers the health from the creature you have just slaughtered into you, so it's like a hospital - only a deadly hospital that kills things too.

BFG [Big err Freaken' Gun].

The mother of all weapons.