Teleportation allows you to quickly change your location on the current dungeon floor, moving you from one square to another (even very distant) instantly. It is one of the best escape tools you will have handy for all life-threatening situations.
You can teleport at will by zapping yourself with a wand of teleportation, applying (and breaking) a wand of teleport, or reading a scroll of teleportation. You can also teleport at random times through the Teleporting status effect, gained by wearing a ring of teleport or through the Teleportitis "disease" (see below). Removing this state is easy in the case of the ring, but tricky otherwise.
You feel jumpy.
Teleportitis is a state when you teleport at random times to random places. You can acquire this state by drinking from a fountain, eating certain unicorn or magic mushroom flesh, or walking through a magic cloud. It will wear off eventually, except for the rare cases when the Teleportitis granted by a fountain is permanent.
Coupled with TeleControl, you can make a good use of this state.
You feel very controlled.
TeleControl is the ability to control where you land when you teleport. The distance from your current position is limited based on your Intelligence. If you try to land past this distance, in an unvisited area, or on top of an obstacle such as a wall or a monster, you will instead be teleported randomly. You can acquire TeleControl by wearing a Ring of TeleControl or eating a Blink Dog corpse.
You feel firmly planted in reality.
Teleport Lock will prevent you from teleporting, deliberately or not. It also prevents your limbs being teleported away by angry gods, and your items being teleported out of your inventory by mystic frogs. It can be acquired from an amulet of dimensional protection.