I love my PSP, I do hear a lot of people (particularilly, one of my friends) bitching about it, and so far they haven't brought up a single good reason for not liking them. I must say, I've got 17 games for it, which is quite a small amount when compared to my other gaming systems, and I've played most of the games on it to death. I would get more, if it weren't for the hefty price tag that they seem to have.
One thing that I have to dissagree with that has been said on this thread, is that 1st person shooters do not work on the system, well I must've played Medal of Honer Heroes for over a year and a half online, that was first person, the controls where great, and it had a pretty good community. Though the second one in that series did suffer from a number of flaws.
On the other hand, one place where the PSP does shoot itself in the foot (certain titles in particular, I'm looking at you Syphon Filter: Dark Mirror!) is the playstation network, I mean, I've been on the phone to them three or four times asking for an activation key for my online account, everytime they've said that they'll send a new one to me, and this is over two years later, still no key. Which is a shame, because whalst I was playing that game on the online trial account, it looked very good.