In Quake 3 and 4 multiplayer, Haste is a powerup that adds 30% bonus to your firing rate and running speed. It lasts for 30 seconds and makes small clouds of smoke form behind your feet as long as you have it. It respawns after three minutes.
Haste, combined with the Rocket Launcher, is a very deadly combination. Not only are rockets much quicker, it's also much harder for an enemy to hit you. The Plasma Gun and Lightning Gun can also make good use of Haste as well; Haste turns both of them into almost hitscan-like weapons that inflict a lot of damage per second.
If you lack powerful weapons, the shotgun is also a good choice due to the more likelihood of fighting the enemy at short distance.
However, use caution while using explosives and BFG10K, there is a good chance that the Haste users kill themselves for being too aggressive.
If you are up against someone with Haste, prepare something with high damage or rate of fire to intercept the user, look for smoke will make finding the user easier. Avoid fighting Haste user at close if your reflex cannot cope with enemy speed or your ping is high.
Look for predictable points, like the exit of the teleporter, choke points and narrow corridor that is difficult to maneuver, ambush Haste users at these locations are often easier than leading your weapon to them while they are on the run.