For when a grenade positively, absolutely, has to be there on time.
The Rocket Launcher, or "RL", is one of the most potent Weapons in Quake. Getting hit by one is a one-hit kill if you don't have any armor, and its splash damage can do the same if you're close to the point of impact. Unlike most other guns besides the Grenade Launcher, this gun will never switch automatically when the player runs out of ammo of all other guns.
In single player, the Rocket Launcher is a devastating weapon. Since the enemy AI is rather unintelligent in its behavior, it's pretty easy to launch Rockets straight at them without worrying that they'll avoid it.
It's also very useful against faraway Spawns, as one explosion can set off a chain reaction that will get rid of most of the Spawns in a room. If they start to attack, don't use it against them, as if you hit them from close-range, you'll feel the effect of the Spawn and the Rocket's explosion.
Don't use the RL against the Fiend and Shambler. The Fiend's tendency to jump means that it'll usually get much closer to you as you're firing the Rocket, and the Shambler takes half damage from explosives.
This is where the Rocket Launcher truly shines. As stated earlier, the RL can kill an unarmored full-health target or newly respawned players with one shot.
The weapon can also juggle enemies in the air via its splash damage; keep enemies away from you, corner them in a bad position and be used to Rocket Jump.
Just remember that the RL's splash damage can hurt you as well, so don't try to use it in tight areas unless you're absolutely sure that you can survive the splash damage, or bear to have some battle scars for the sake of Rocket Jump.
Unless you're a really good shot (and the enemy is unable to dodge), try to aim at a target's feet. While the splash damage may not kill them in one hit, it'll cause enough damage so that the next shot will kill them and will usually toss them away from you. Getting cornered by an airjuggle is a really bad position to recover from, try to take no chances.
Once target is airborne or tossed away from you at the open, try to take them down with the Nailgun or Super Nailgun until they get to where your RL can be effective again. Alternatively, one can also launch them into the air with the RL and finish them off with the Shotgun. At medium distances, most of the pellets will still hit the player and deal good damage, allowing for a quick kill.
Rockets are slow projectiles but still fast and devastating enough if you run into someone wielding it. Try to anticipate your target's movement before firing. Depending on range a little amount of leading at distance will help on landing a devastating blow. Prefiring with panic and missing it may put you in a disadvantage on a one on one combat, try to position for height advantage or take cover.
Leading the shot with wrist flicks can be effective when either foe or you are getting closer or trying to keep distance. Especially effective if you can predict the movement of the opponent you can land a direct shot to their guts.
Remember, rockets will stall between your movement as their projectile speed require a certain flight time to reach a target. Try to compensate and lead the shot further by aiming with the wings of the crosshair if you expect foe to retreat away.
Rockets pack devastating blows, dodging them is throughly encouraged and rewarded. By strafing a straight line, opponent can be baited into leading their shot at that direction, first. By that time reacting with a diagonal step will get you steer clear from the path and deny the shot. Hopefully you'll be out of its blast range when you dodge too. Just remember to keep focused, and there'll more than one shot to evade in a match.
Death by Own Rockets
"Player" becomes bored with life
Death by Enemy Rockets
"Player" rides "Attacker"'s rocket
"Player" was gibbed by "Attacker"'s rocket (if target is gibbed)
As part of promotion for Quake 4, Team Fortress 2 added this weapon for the Soldier class, known as The Original. Though technically a reskin of his stock Rocket Launcher, it includes the sounds of the Quake weapon, from the firing to the explosion sounds. The viewmodel is also at the bottom-center of the screen, similar to Quake.
The name of the weapon in TF2 is a reference to that it's the original Rocket Launcher of the Soldier class, due to the original Team Fortress being a Quake mod, before being picked up by Valve.
Rocket Launcher being fired
Texture map for world model
Texture map for view model
Texture map for the Rocket
The Soldier from Team Fortress 2 holding this weapon, known as The Original, during Quake 4's promotional period.