Will a PSP 2000 case fit on a PSP 3000?

It might if it is soft. The PSP-1000 is thicker than the PSP-2000, with two protruding bumps either side at the back. The PSP-2000 by comparison lies flat at the back, due to the thinner battery. A PSP-1000 would probably not fit in a hard case designed for the PSP-2000#s flat back, but a more flexible case might accomodate it.