Teleportation, the idea of moving from point A to point C without traveling through the space between, has been around for thousands of years, the first recorded claim of teleportation coming from Buddhist history, in which the Buddha was reported as teleporting between his home in India and Sri Lanka, and later back.
Two kinds of teleportation have been identified in fiction. In one, the item to be teleported is broken down into its component atoms, typically to translate it into energy or a fast moving signal, and reassembled on the other end. People have pointed out that this means that teleportation of a person is killing them to replace them with an identical clone that has the same set of memories. If this kind ever exists, I think that I will not teleport myself, but that it will become routine to teleport objects. If I buy something at the hardware store, rather than put it into my car and drive it home, I will teleport it directly home, and then drive there alone. Vehicles will only be required for the transportation of living things. This would be a big advantage to me, since sometimes I buy things at home improvement stores that are very difficult to fit in my smallish car.
In the other, space is bent, causing an extreme shortcut between point A and point C, the item to be teleported is pushed through this shortcut, thus bypassing all the point B that is in between the two. The space is then un-bent. Since the item remains intact at all times, it would be safe to teleport people using this system. This may have some strange energy requirements, and repeatedly bending and un-bending space can't be good for it.
In any case, either of these teleportation systems would revolutionize the world forever if done reliably. For one, transportation is now obsolete for anything not alive. Sure, your factory could pay a truck to haul it to the store, as is done now, but it will almost assuredly be cheaper to just teleport the widgets over. The transportation industry's loss will be the rest of our gains, as this will mean lower costs, which could lead to lower prices if the extra money is not simply absorbed as extra profits.
But more noticeably, space travel. The international space station was painstakingly built over years, with many rockets each hauling up one additional part until today's current structure, the size of a football field, was in place. With teleportation, the entire structure could be built on earth and then teleported into orbit. Even if the teleporter had to supply the difference in potential energy, which seems like a certainty if there's anything realistic about this at all, this would cost far, far less than all the rockets that were required. If you're using the reassembling type, the astronauts would then have to travel up by rocket, but when they arrive, all of their food, tools, scientific equipment, and computers are all already in place. If you're using the portal method, the astronauts could just directly teleport to the station, and rockets would be obsolete.
And space colonies could be constructed on earth's most brutal deserts, like the Atacama desert on the Peruvian/Chilean border. When we verify that the station is able to sustain human life, it's then teleported to a distant planet, such as Mars. Humans arrive there, either by rocket or portal, and teleporters allow the exchange of goods between earth and the colony. Even if energy can't be directly teleported, fuel or charged batteries could, and if signals can't be teleported, then UUCP commands over a small, say, USB stick, could.