I'm collecting PSP games myself - not everything is brilliant, but I get 3 times as much use out of the PSP than I do with anything else, including the 360 recently.
When I first got the PSP, I didn't get on with it at all. I found it clunky, most of the games were not to my liking (there were some great ones but nothing I couldn't enjoy on other consoles) and it just wasn't the handheld I wanted. Traded it in and didn't really miss it. Last year they had the silver Slim and lite at work for a silly price, so I took a chance, and this time it started to make sense. To top it off, recently bought an old style PSP off a mate for emulating, so have also now got into that side of things; but it's still the content made for PSP that is my major reason for liking the machine.
Also, a lot of the more recent releases have been more interesting, for me at least, than some of the 'big' console versions they are based on. 2010 World cup, F1 2009, Littlebigplanet, Mod Nation Racers, WWE 2010. I'm only at about 65 games at the moment, I traded some in to make room for others, but there's an endless supply of games that I'm after. The retro comps are also, imo, absolutely brilliant.
It's also the console that has made me appreciate game genres and franchises that I've either not bothered with or not appreciated before. Castlevania (Dracula X Chronicles), Kingdom Hearts (Birth by Sleep), Ridge Racer, Power Stone.