Every once in a while, I come across a website that talks about the way Star Trek (and some other misc sci-fi) transporters work. They often conclude that transporters actually work by disintegrating you, then making an exact copy at the destination. Which of course brings up a thousand other questions. If it were so easy to copy a person, why would people have to die at all? Why not just backup all your crew members every day like you do with any other data? Even disease, lost limbs, etc, could be cured through transporter use. Why kill the original crew member? Why not just send down a copy, have him complete the mission, then disintegrate him, without ever disintegrating the original on the ship?
Here's my opinion. Mind you, this explanation is silly and unscientific, but no more so than most Star Trek technology. Basically, in the Star Trek universe, they have discovered how to convert matter into energy and vice versa. The reason they aren't killing you is because it's the same energy particles being converted back into matter. So first the transporter changes you into energy particles, atom by atom. Then those particles are shot to another location (much like a phaser shoots a beam of energy), then those same particles are converted back into matter, atom by atom. If someone simply recorded your transporter pattern and made another you using any old energy, that would be a copy. But since it's the same particles being temporarily transformed from one state to another and back, it's still you.
This is supported a little bit by the fact that you can't beam through shields. You can still send data through shields; enemy ships often communicate with each other. If a transporter pattern were just normal data, you could send it to the other ship just like you send a communication signal. You can't shoot phasers through shields either. So, maybe transporters work more like phasers than communicators, in that they fire energy rather than just data.
In a few episodes, the crew members mention experiences they've had during transport. There was an early TNG episode where they did a "near-warp tranpsort", and a crew member mentioned feeling like they were in a nearby wall for a second. A much later episode had Barclay wrestling with monsters in the transporter stream. While these are some of the sillier examples of the way the writers have abused the technology, they do support the idea that the energy particles themselves are still alive and retain some aspect of the matter converted.
Also, they often beam straight to a remote location (rather than another transporter pad). To me, this means that when they start the conversion process, the conversion back is inevitable. Meaning, your body is turned into energy particles that are only meant to stay energy particles for a few seconds before they turn back. So it is your actual pattern being sent across space, not just data waiting to be reconverted from random energy particles at the destination.
Admittedly, one thing that doesn't fit is Thomas Riker. If they'd established that one was "real" and one was a copy, I'd be fine. But they seem to imply that both are 100% Riker. When they boosted the signal that split his pattern, they were adding non-Riker particles to the Riker particles, which means that either one is made from pure non-Riker energy, or each of them is now only x% Riker. Though perhaps, every time someone is transported, a few atoms are lost and replaced with those from random energy. But since your body replaces cells all the time anyway, it's no big loss. So right after the accident, both Rikers were only 50% Riker (more or less) for a while. But ever since then their bodies have been replacing their own skin cells, so the now each of them is closer to being 100% real.
Again, I admit this is all Insane Troll Logic. But to me it makes more sense than the Federation routinely using a system that involves killing people and copying them.