Derezzing

Derezzing is the phenomenon that occurs when dead players, vehicles, turrets, weapons, etc. are removed from the map after a short period of time.

From a real life perspective, derezzing appears to free up computer memory. Another reason is that growing amounts of dead bodies could influence the gameplay.

Unreal and Return to Na Pali
In Unreal and RTNP, derezzing isn't present, and dead bodies remain in the game.

Unreal 2
In Unreal 2, fallen enemies lie for a short while, in some cases emitting a blue glow for a short while, indicating Shield reserves the player can use to refill his own supply if he is quick. Soon after bodies sink into the floor or ground. This phenomenon isn't explained in the story.

Enemies hit with explosive weapons are usually gibbed.

Unreal Tournament
In UT bodies don't disappear, but can be gibbed with explosive weapons.

Dropped weapons spin and shrink. If the player is quick, he can still pick up the weapon during the animation.

Unreal Tournament 2003 & 2004
In UT2003 and UT2004 live players can be gibbed, but bodies cannot. Even gibbed players leave part of their lower body. This part, of the whole body, derezzes with a graphical effect that turns the body's surface translucent with pulsing green signal traces like those on a printed circuit board. The body slowly rises from the ground and soon disappears completely.

Dropped weapons disappear like they do in the original UT.

In UT2004, destroyed vehicles leave a burned chassis which simply disappears after a short while.

Unreal Tournament 3
In UT3 ...

Dropped weapons disappear like they do in the original UT.

In UT3, destroyed vehicles leave a burned chassis as well as a number of pieces broken of at the time the vehicle was fired upon. All the pieces soon disappear with a glowing, orange effect on the surface that looks somewhat like paper being burned.

Unreal Championship
See UT2003 & UT2004.

Etymology
The verb "derez" comes from the film Tron, where it is a short form of the word "deresolution". If somebody or something is derezzed, it is destroyed.