PSP Eboots
Official Eboots
Download PSN PS1 games from Sony servers (registration required)
Official Eboots have superior compatibility, but their number is really low.
Converted Eboots
Convert your own PS1 ISOs into Eboots using PSX2PSP
Pre-converted Eboots
PSPISO (registration required)
Popsloader
If you are having some trouble with converted eboots, be sure to download popsloader here. Most of the games will work without it nowadays, but for those that don't, you'll need this. See popsloader compatibility list.