I went through the training and then my company paid for me to go to Carnegie Mellon and go through the PSP instructor training course to get certified as an instructor. I think the goal was to use this as part of our company's CMM/CMMI effort. I met Watts Humphrey and found him to be a kind, gentle soul with some deeply held ideas about process. I read several of his books as well.
Here's my take on it in a nutshell - it is too structured for most people to follow, assuming you follow things to the letter. The idea of estimation based on historic info is OK, particularly in the classroom setting, but in the real world where estimates are undone in a day due to the changing tide of requirements and direction, it is far less useful. I've also done Wide Band Delphi estimation and that was OK but honestly wasn't necessarily any better than the 'best guess' I'd make.
My team was less than enthusiastic about PSP and that is part of the problem - developer buy-in. My company was doing it for the wrong reason - simply to say "hey, look we use PSP and have some certified instructors!".
In the end, I've found using a 'agile' approach to be better. I have a backlog of work to do and can generally estimate it pretty well. I've been doing it long enough that I can make pretty good rough estimates on time and frankly don't think that the time tracking really improves things much. Perhaps in some environments it would work well, but at my place, we'll keep pumping out quality software without all the process hoops that yield questionable benefits.
Just my two cents.