Qaz from DCEmu (registration required) has released a pretty nice AIM/MSN/Yahoo client for the PSP. It's pretty easy to install and use ... so long as you're willing to struggle with the PSP's pathetic phone-like virtual keyboard. Too bad ZX81's newly released Virtual Keyboard isn't compatible: certainly, conversations would be far more manageable. Regardless, these are two appreciated apps that will certainly help a great number of people, especially because it doesn't involve homebrew. Simply download, extract, and access from the PSP's internet browser.
Make sure the URL you input reflects where you placed the files.
The Virtual Keyboard will only work with inputting URLs, or for Google searches. Better than nothing, right?