There is AdHoc Party for PS3, which allows you to play some AdHoc (local) games on the internet.
The PSP does have WiFi though, and there are a lot of games that have online (infrastructure) multiplayer.
If you don't have a PS3, you can still play some adhoc games online with Xlink Kai. It works similarly to Adhoc Party, but instead of a PS3, it requires a compatible WiFi dongle instead (there is a plugin that lets you use the psp's usb connector instead, but that doesn't work on every game.)