You'd have to buy/borrow the game.
When I was researching before buying my PSP, I heard PS1 compatibility is near 100%.
So far, I've only tried FF9 and Tony Hawk's Pro Skater 2, but both work perfectly with no slow down or glitches so far.
That the PS1 compatibility is near 100% is because it's made by Sony, they use it to sell classic games via PS3 to your PSP or something from what I've understood.
There are N64 and SNES emulators, but from what I hear compatibility is iffy. (Haven't tried myself yet because I barely got my PSP.)
I think SNES compatibility on the PSP is better than the DS though.