Teleportation, the movement of objects from point A to point C without passing through the space between, actually does happen, on the quantum level. Individual atoms have been known to teleport around, though macro-sized objects, things at our level, do not. Developing some means of actually doing so would revolutionize hundreds of industries, from manufacturing (why weld when you can just teleport the steel into the right places) to transportation (Instead of bothering with boats and trucks, goods are teleported from the factory that made them to the store that sells them....or even to the buyer's home) to mail (the post office only needs one facility now: teleportation central).
Attempts to bring this to fruitition often involved some very strange ideas indeed. There was a guy who was popular when I first came to the internet, and surprisingly is still around. Alex Chiu, a rather odd businessman and philosopher, was hawking his "immortality rings," which appear to be some sort of re-machined industrial washer that he then magnetizes and claims that it provides immortality to the wearer. Wouldn't the world be crowded if everyone was immortal, people asked him? He responded in the affirmative...and then answered that a teleportation machine that he invented. It involves a series of coils, which according to Mr. chiu's beliefs about atoms, would convert the atoms into a signal which could then be transmitted to the receiver. I find this idea strangely popular, especially with string theorists.
If human-sized object teleportation is possible, by what means could it occur?