Any idea whether Leopard will run on a 1 Ghz PowerPC G4 eMac with 768 MB SDRAM (running OS 10.4.8 now)?
Yes... but if we tell you we'll have to kill you. Actually, extrapolating from several things... the fact that Tiger (X.4.8 runs well on a 400MHz G3 with 384Megs, the iPhone is running OSX Leopard, and the observation that every upgrade of OS X has run faster on the same hardware than the previous version... I think it will run fine.
I think it would work okay on that machine, but a memory upgrade to 1GB would improve performance.