There are a few categories of weapons in Halo3: Human Weapons, Covenant Weapons and Forerunner weapons

Human Weapons

Human weapons a pretty standard. If you have played any 3rd or 1st person shooter, or watched an action movie, you know these weapons already. The spartan laser is the weapon which is futuristic. The battle rifle is different from standard, realistic weaponry as well.

Battle Rifle - this is said to be one of the better weapons to use in the game. Unlike a normal rifle, it shoots three rounds at a time.

SMG
Assault Rifle
Pistol
Shotgun
Sniper Rifle
Rocket Launcher

Spartan Laser- The Spartan laser is a beam which can penetrate multiple humanoid targets with a beam of energy.

Covenant Weapons

Plasma Pistol

Plasma Rifle

Carbine - the carbine is the plasma-based equivalent of the battle rifle. The big difference here is that the shots from the carbine can mark a target, making him much more visible.

Needler- shots projectiles into its target, causing massive damage.

Beam Rifle

Fuel Rod Cannon - it is similar to an rpg, but it shoots balls of plasma

Energy Sword - This is a close quarters weapon. You basically get to shank a fool with this.

Brute Weapons

Spiker - This is basicaly like the carbine or battle rifle. Has a high rate of fire

Brute Shot - this is a grenade launcher weapon

Mauler - this weapon is sort of like a shotgun, if it was the size of a pistol. It can be dual wielded.

Gravity Hammer - The gravity hammer is a melee weapon that will send enemies flying when it is swung down. It can also deflect grenades and rocket fire in some cases.

Forerunner Weapons

Sentinel Beam - this is a rare weapon which shoots an orange beam. it has infinite firing range.

Support Weapons

Grenades