I brought my PSP to the "World" during our April trip. We left it in the room each day but it was used extensively during our "in room time" and on the trip down. I did only see one other person with a PSP during my stay in Disney. It was a little kid on a bus from Downtown to Boardwalk.
I don't know that I would take a PSP to the parks as there is just too much of a chance for it to be stolen, dropped, gotten wet, etc...I invest too much in my gaming devices to let something like that happen to it. (Yes, I'm a 37 year old man and have an XBox, PS2, Gamecube, Gameboy, PSP and Nintendo DS).
Regarding bad PSP's. I have heard quite a bit about that but I lined up to pick up my pre-ordered PSP at Midnight on March 23rd. First one out of the box worked fine and I have had no problems with it. Check out the messages boards over at sony.com and you can chat with others that have had bad luck with their PSP's.
Sunking