I've written about the Pew Research Center's recent study of American attitudes towards future technology. One of the more controversial ideas in the study is teleportation, with only 39% of respondents expecting us to have invented teleportation by 2064.
We've already invented (or at least discovered) one kind of teleportation: quantum entanglement, which a team of Austrian physicists has recently perfected to 103 dimensions using only two protons. Our growing understanding of entanglement can be really useful in quantum computing, but there's a big difference between transporting protons and transporting matter, and between transporting individual molecules and transporting systems.
And if we ever start trying to transport people, a bigger question emerges. Michio Kaku outlines it here:
We have no reason to believe that the teleportation of a human being would preserve continuity of consciousness. The old ship of Theseus paradox comes to mind: most of us wouldn't say that somehow cloning ourselves using quantum technology would make us wake up in the new body, so why would destroying the old body—as teleportation does—make us wake up in the new, teleported body rather than disappear in the residue of the body we left behind?
As Kaku points out, this is really more of a theological question than a scientific one—and, like most theological questions, is unlikely to ever be definitively resolved. Kaku uses the example of Star Trek's Captain Kirk above, but it's worth mentioning that even in the fictional world of Star Trek, there were characters who really hated the idea of having themselves or their loved ones transported. If the technology for human teleportation is ever developed, it may meet the same kinds of bioethical objections that human cloning, late-stage abortion, euthanasia, and other controversial medical issues have raised.