PS1 emulation is one of the most anticipated features for the PSP at the moment. You'll be able to download Riiiiidge Racer, and other PS1 classics to your PSP and play them on the go.
Sony has been taking their time, and we've been waiting for any new information on things like price, available games, and interface. It appears that the homebrew community is sick of waiting-- it has just released its own emulator. Yoshihiro's PSX-P emulator will let you play bootleg PS1 games on the go, although the code is somewhat rough at the moment. To run it, you'll need an eLoader, which now supports firmware as high as 2.71. For more information, visit http://www.pspfanboy.com/2006/09/24/homebrew-playstation-emulator-reaches-beta/