Teleportation
Teleportation is the act of making an object instantly disappear in one location and reappear in another. It is fairly common in sci-fi and fantasy, though the exact method used can vary quite a bit, from wormholes to alternate dimensions.
Teleportation is possible real-world with subatomic particles in the quantum world; it's kind of how semiconductors work, so transistors like the ones in the computer you're probably reading this article on.
Problems accrue if you get your teleportation end co-ordinates slightly wrong and you end up five hundred feet in the air or inside a cliff. Or, if you share your teleportation start area with a fly.
In Gaming
Warhammer 40,000
Teleportation's possible in Warhammer 40,000, but isn't really a pleasant thing to do since it basically involves making a short jump through the Warp. It can be done either through technological means with a device known as a Teleportarium (if you're a human in the Imperium) or Tellyporta (if you're an Ork), or through the use of psychic powers. Needless to say even going through the Warp for a Little While has it's risks. The danger's mitigated by the use of Teleport Homers and a highly skilled psyker.
Necrons have no need of the Warp or psykers to move instantly between locations, as their technology's just that much more advanced compared to the other races, and can tell the laws of physics to bugger off.
Star Trek
Teleportation's a common technology among all spacefaring powers by the 23rd century leaving aside some podunk regions of the Delta Quadrant. It's usually quite safe, though it can be quite finicky and can be stopped by a wide variety of things from jammers to electromagnetic storms. To explain why characters don't wind up a few inches shorter or vaporize into nothingness when they're transported, technobabble in the form of the Heisenberg Compensator was introduced during The Next Generation.
Dungeons and Dragons
Powerful enough spellcasters and magical beings can use one of the eponymous spells or assimilated. Some spells come with a chance of ending up in the wrong place, depending of the nature of the spell and how familiar the caster is with the place he wants to end up. In 3rd edition most Demons and Devils can teleport themselves and a small payload at will.
In Eberron, the Dragonmark of Passage has various teleportation abilities past the least mark. The short distance for all but the most powerful (and rare) marked heirs means it's not too useful as a service for anyone but the obscenely wealthy, but in response to the rise of Airships, House Orien has been working on a network of teleportation circles that will overcome this limitation.
Low-level versions might include Blink, where the teleportation only gets you or your dog a few feet away. Teleport is often fifth-level or higher given its ability to fuck with a linear plot.
WARNING: the DM is well in his rights to rule that Teleport does not work everywhere. Nobody wants a crew of illithids 'porting into the council-chamber with their pet tarrasque and 'porting out again sans monster. If this spell is readily available, reasonably-intelligent and powerful civilisations will be aware of it and will take steps against it. An excellent example is D1-2-3: Drow Trilogy: the drow simply set up their Vault down where Teleport barely works. Other magical wards (aboleth are handy with glyphs) will be set up in similarly-sensitive regions.