you can use nes emulators for amiga to run nes roms. finding the roms online is tough and most of the emulators arent that great but they do work. i have run some roms on an a1200 with a 50mhz 030 accelerator.
ShapeShifter is close to perfect, according to me, but I haven't used it to the extent that I've tested its limits, so I wouldn't know.
AmiMastergear runs mostly all SEGA Master System and SEGA GameGear games without any problems at all (I'd say that 95% of all the games I've tested have had zero to close to no glitches at all, running at full speed on my 060 and most of the time in full speed on my 030).
AmiMSX is also a very very good emulator (a shame that he who made those AmiXXX emulators stopped developement, since they are really great stuff!).
Besides these, I don't really know of any good emulators for the x86 Amiga. Which have missed out on?