As we mentioned lasat issue we've been reading this great  Star Trek book that describes the fictional Enterprise.  Whenever this subject comes up, people always ask me "Did my people have transporters?"
The answer is yes, but they worked on a completely different principle.
Our systems were beam tubes. A hollow beam of energy was created that was accellerated up to two-hundred times the speed of light and sent to the receiving station either on an orbiting ship, or, on another planet, usually a nearby moon.
The person to be transported stood on a grid that temporarily caused their atoms to become de-bonded.  When they reached this state they were sucked into the transport tube by the flow of energy and carried by it to the arrival chamber at the receiving station where their atoms simply pulled themselves back together!
The person was never broken down molecularly as the transporters in Star Trek are supposed to do, and departure and arrival stations were necessary.  We could not transport through solid matter, though one way beam down was possible to open areas.  You could not beam back up again until a bus arrived with a transport system.
As I have said before, the similarities between the fictional space ships and real ones are incredible, but the differences are also profound.