Can I play downloaded games on my PSP?

Hello, I recently bought a PSP off eBay.But since a lot of PSP games aren't for sale anymore, and I don't wanna go through the trouble of buying them all, I was wondering if I can play downloaded games on my PSP? Do I need to hack my PSP or do something else?It's a slim type PSP by the way, model number is 3004.

Yes, you can play pirated games on a PSP.
Joel16 has an extensive guide in the Tutorial section on how to hack your PSP. Not having a PSP myself, I can't really help you much on the topic, but I'm sure there are others that can give you a hand.

What kind of PSP did you buy a go or the Fat PSP?