Thumps neat exploding bombs into the air. You can even bounce a grenade off the wall or floor. When a grenade hits someone, it explodes. If it misses, the bomb sits on the floor for a moment, then explodes. Even though I sometimes bounce grenades into myself, this gun's still my favorite.
The Grenade Launcher, often shortened to "GL", performs as its name implies; the grenades will explode if they hit a target or after a few seconds on the ground. Grenades can be used to Grenade Jump. The Grenade Launcher uses rockets for ammo. Unlike most other guns besides the Rocket Launcher, this gun will never switch automatically when the player runs out of ammo of all other guns.
In Single Player, the GL can be used like the Rocket Launcher until you actually get a RL. It does good damage against every enemy except the Shambler as it takes half damage from direct grenade explosions.
The GL really shines against spawns. Find some spawns that haven't noticed you and fire away with the GL. With the grenades plus the exploding spawns, you should be able to clear out the room within a few seconds.
Try to bounce grenades off walls if you can. Since most enemies are quite lacking in their AI, most of them will run into the area that you're peppering without any second thought.
The Grenade Launcher, along with the Rocket Launcher is usually an ideal weapon for fighting zombies. The explosion will often gib them, preventing them from reviving themselves.
At medium ranges, the Grenade launcher can deal more damage per second than the Rocket Launcher due to its faster firing speed. Shots fired from the Grenade Launcher also don't have slight damage fall-off over distances like the Rocket Launcher projectiles do.
The GL is less effective in MP. Because of MP's fast pace, it's very difficult to set up a "traditional" (toss a few grenades and wait at an area) effective grenade trap (unless you fire the grenades into a tight hall). Since the GL uses rockets as ammo, you shouldn't use it if you plan on getting a RL anytime soon.
The GL is really useful for covering retreats. As you're running away, fire some grenades at the opposite direction. Your attacker will either stop his pursuit or get gibbed by the grenades.
It can also be used to cover areas that you're trying to hold, such as a room that has a quad damage. Toss a few grenades around the area, and you should catch anybody trying to come in off guard. Then, finish them off with another Weapon.
Note that grenades pass through whomever fired them; they do not explode upon contacting the owner. Thus, a grenade per se is not harmful to the owner, but the explosion can be.