Very versatile device, you have to ask SoulQuarian he can give you an elaborate rundown. He LOVES his PSP. It can do so many things I was unaware of. A very good choice, you will definitely get some use out of it.
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It's got a LOT of potential, but it's best if you're interested in homebrew software (aka running emulators of systems past on it) or don't have a laptop and want something to get by watching videos and browse the web with.
As far as the actual games that are actually made for the PSP go, there's been nothing worth talking about aside from Lumines, Grand Theft Auto, and SOCOM.
I really like the PSP as a system, honestly. But as much as I admire it I have to call a spade a spade and say that the DS just blows the pants off of it in the current software lineup. Just to name some titles: Advance Wars, CastleVania, Mario Kart, Trauma Center, Nintendogs, Phoenix Wright Ace Attorney. Not all these games will appeal to all tastes, but they cover a wide palatte of options and there's guaranteed to be something you like.
Emulation is the saving grace of the PSP, if you don't care about games from the first half of the 90s then I'd skip it for now.