Sony has announced a legal PS One emulator for the PSP to be released with a feature firmware update.

From IGN:

PS Biz Brief 06: PSP E-DistributionDownload and play PSOne games.by Chris Roper

March 14, 2006 - Sony's Ken Kutaragi continues to drop PlayStation Portable news during the company's PlayStation Business Briefing 2006 as he's just announced that the PSP will see "E-Distrubution" features added sometime in the future.

Users will be able to boot software directly from their Memory Stick, all official-like this time around (you know what I mean). The first major announcement for use of this will be a series of PSOne games - yes, you will be able to download classic PlayStation titles and play them on your PSP. No word yet as of whether or not you'll be able to transfer games directly via disc or not, or which games we should see first, but more news on this as it comes in.

http://psp.ign.com/articles/696/696052p1.html