Here's a very positive piece of news from Sony Computer Entertainment's Gamers Day: Sony revealed how PS1 games would end up on PSP's memory stick.
The PSP will get its games from the PS3. Instead of building a network specifically for the PSP, or trying to connect the PSP to Sony's Connect service, gamers can log into the PlayStation Store using their PS3, find your favorite PS1 games there, buy and download them, and then enjoy it on your PSP.
IGN speculates that that the PlayStation Store will also be integrated into the PSP in a future PSP firmware update. For now though, the console is integral for digital distribution. A number of PS1 gamers are already listed on the PlayStation Store.