I was just talking about this with a friend the other day: teleportation, also, faster-than-light travel - and which of the various means proposed in fiction were more plausible to less plausible. The actual course of the conversation is too circuitous and discursive to reproduce, but I thought I'd share some of the conclusions and upshots, for the sake of any who may share an interest.
We both agreed that a Star Trek style transporter would kill you. Little consolation to be had from the sudden existence of an exact duplicate of you, even if the duplicate is so close a copy that God, probably, couldn't point out any material difference. Still this would be a new person, a consciousness instantly beginning its life in the middle of your previous uncompleted thought, stepping blithely out of the other transporter chamber with every one of your same connections recreated and hence, all your memories, your personality. Not with them "intact," but rather, with them reproduced. But the you who you were would fade to black. Show's over. No after-credits sequence.
(We also discussed the likelihood of various scenarios in a given sci-fi universe where God exists, and superintends a more-or-less traditional God-style setup. Imagine the plethora of Captain Kirks rubbing elbows in the afterlife, each with a full memory of everything up to their incarnation's first transporter trip! This would include all of that incarnation's memories brought along from all earlier Kirk's trips - indistinguishable from its own brief life's memories! For some people, a heaven indeed. That's not even counting all the Rikers.)
Now, my friend hadn't seen The Prestige, so I couldn't bring in that comparison - and by the way, if you haven't seen The Prestige, spoiler alert! Skip to the following paragraph! It's same principle at play, except 1) the original is not automatically destroyed, and 2) where Star Trek leaves it unspoken, glossed over, in The Prestige the implications of being erased here and remade there take center stage: the you who you really are always falls through the trapdoor and dies. The you who you never were (and never will be) always appears, an instantaneous, new creation, blinking into brand-new being at some remove of distance.
Such borderline metaphysical considerations aside, it's hard to really say how soon or whether the actual transporter hardware can be realized, not without reference to some proposed method. Just how is a beam of energy to build such a complex structure? It's not gone into. Unsurprisingly, most depictions of teleportation don't really get into the mechanics of what happens. Whether turning matter into a signal to beam to a distant location, tunneling through tesseracts or wormholes, or routing one's self instantaneously through adjacent, overlapping dimensions, even when they get into the "how," the how is rarely presented as anything our understanding of reality could call plausible. Naturally, that doesn't mean we won't get there! But we can see in each case what the challenges will be: here we need some exotic element of matter that, as yet, appears nowhere in the periodic chart. There, we need some novel form of energy or force which doesn't appear to be part of our baseline reality at all - or a way to make our known forces behave in novel ways. Such limits are hardly trivial, and we must accept the possibility we may not overcome them if the materials and means for a given method to work simply aren't part of what reality's operating parameters support.
But then again, maybe we'll teleport back from a future where the problem was solved, and lay the secret bare to our previous ignorant selves! As clear as transparent aluminum.
For the record, out of Star Trek tech mainstays transporters, warp drive, deflector shields and...some fourth thing, I forget what...deflector shields seemed (or were agreed to be at least) the least likely to be realized, or realizable, within the limits of known physics - at least as depicted. But given the distances involved in space combat, we both agreed that if space-warping technology could be made to work, it could be adapted to serve the purpose. If you could project a decent-sized defensive warp bubble out to a fair range beyond the ship's hull, one that increases the angle of any incoming light or high-velocity matter, that would do the job neatly. A refractor shield, as it were.
But of course, whether for purposes of travel or defense, creating the warp bubble itself is a bit problematic - a problem shared with other proposed methods of FTL travel. Exotic materials that don't exist, or amounts of energy in excess of the total sum of all energy and matter in the universe, are required.
A tricky nut to crack!