Jumping is a basic movement technique in most, if not all, modern shooter games. In the Unreal series of games, jumping is used exclusively for gaining height and does not provide any additional horizontal speed boosts, which is what dodging is used for. There are, however, a few advanced movement techniques that involve jumping.
Various Unreal games provide the Jump Boots power-up to greatly increase the player's jump height.
Double Jump
A double jump is a jumping move performed in mid-air, which was introduced in UT2003. It can be performed at the apex of the movement parabola to increase the total jump height. In UT2003 and UT2004, a double jump can be performed once during any kind of air movement, in UT3 only if the air movement wasn't started by dodging. The Quad Jump mutator increases the possible number of mid-air jumps to three during any kind of air movement. If you jump right after walking over a ledge you actually perform this mid-air jump, which is why you can't actually do a "double jump" in that case.
The double jump after a dodging move is called Dodge Jump. In UT3 the dodge jump is no longer allowed. If the player has the Jump Boots, they can be activated with a double jump. Despite the restriction of the dodge jump, the Jump Boots can also be activated like this after a dodging move.
Impact Jump
Releasing the Impact Hammer's or Shield Gun's primary fire towards the ground and jumping at the same time will combine the jump movement with the backward momentum of the melee weapon, resulting in a much higher jump at the expense of some health. For maximum height, the weapon should be aimed straight down. For maximum distance, it should be aimed down about 45 to 60 degrees and you should also run backwards. This makes timing the impact jump a little harder, though. In UT2003 and UT2004 you can even try "impact dodge jumping" if you need even more distance.
The impact jump is UT's replacement for other games' rocket jump. Attempting to perform a rocket jump in UT will mostly hurt and hardly push you anywhere. The closest thing probably is a "ripper jump" performed with the secondary firing mode of UT's Ripper or a "shockball jump" performed with the secondary fire mode of the Shock Rifle, though an impact jump outperforms both of them while at the same time drawing less health.
Lift Jump
Another interesting, easy-to-learn and (mostly) painless to perform technique is the Lift Jump. If you get the timing right, jumping from a lift while going up will combine the lift's speed with the upward movement of the jump, allowing you to reach areas otherwise only accessible with Jump Boots or flying vehicles.
Be careful where you land from a lift jump. This type of jump can catapult you high enough to actually take falling damage, especially when combined with an impact jump.