I don't think we'll see PSX running on PSP very well... but apparently the N64 is easier to emulate? Somehow I feel it's more likely we'll see N64 before PSX. Xbox runs N64 better than PSX, I think when i used to fool around with PC emu's for the two the N64 one seemed to run better as well but I'm not sure. If I remember right, the N64 was actually less powerful than the PSX in some ways, like it couldn't display as many poly's at once, but made up for it with hardware effects like texture filtering (the 'blurriness' N64 is best known for) and others. I think the N64 takes less processing power to emulate though.
Just going on the PSP's hardware specs, processor speed, RAM, and video hardware, I'd say we're likely to see everything up to SNES running perfectly, possibly Neo Geo and Mame up to mid 90's at least? All the good 2d stuff really, likely to get GBA as well, but I'm betting 3d stuff will be limited and probably not full speed in most cases if at all. I thought the most powerful pocket PC's, 400Mhz ones, were still struggling to get PSX at like 10fps or something like that?
And I have NO doubt it will be cracked at some point, the only question for me is, will it be a software hack, that we can run off the mem stick, or a retail manufactured disc like a gameshark or one of those devices, or will it require actual hardware modifcation like a mod chip?