How is it I've never heard of this before?
Sounds like maybe it could be something that's part of the Adobe Product Improvement Program, which "transports" information about how you use Adobe products back to the mother ship where grays look it over.
In Photoshop, try Help - Product Improvement Program, and opting out. Let us know if that stops it, since this is just pretty much a guess by me.
Edit: A search turned up several copies on my system - one in the Bridge installation folder and one in the Photoshop installation folder. That implies you might have to turn it off in multiple places (assuming it's the culprit).
LogTransport handles sending crash reports and PIP (product improvement program) data to Adobe's servers.
It should only have pointers to the log files and it's own binary.
And it should exit as soon as it has transmitted the logs (or timed out after a few minutes if the servers are unreachable).
Well, unfortunately it doesn't.
It still keeps on running even after I close Photoshop and worst of all it keeps handles on certain folders or files that I worked with in Photoshop, so that later I cannot delete these files or folders.
I had to figure that out using Process Explorer. Once I force-killed the app, everything was fine again.
Again, it can only keep busy the files and folders involved in the data it is reporting, plus it's own binary.
And I've never seen it hang around more than a few minutes.
Of course, force killing it means that it is probably accumulating more data and is going to take longer to send it all.
Let's not forget the possibility it may have become infected with malware.
Well, to be perfectly honest, I really don't care what it's doing or why. It's a pain in my a** and I'm permanently deleting it from my computer.
Don't delete the executable, or you'll end up not being able to successfully apply a Photoshop update in the future.
Disable it via the means I described above.