@coinage
I'll assume that you mean pure emulators (not, for instance, OS4's 68k emulator) and I won't include Amithlon as it's not legal. That leaves WinUAE/UAE, which is more compatible than any real Amiga (no need to run a degrader - just change the config - and you can get 8Mb chip RAM :-) ).
I've never seen anything that won't run at all on UAE, although I'm sure there must be a few games/demos utilising various non-emulated quirks of the custom chipset. Simcity 2000 runs slowly on my 1.1Ghz PC (but faster than my 030 Amiga, and I'm sure a faster PC would manage it fine). Quick colourfading on demos also seems to suffer, but again probably works fine under a better host PC. I don't know how well it copes with networking as well (AFAIK the BSDSocket emulation just connects you to the internet, not any old LAN) I'd say that UAE/Amiga Forever is virtually 100% compatible.
@Aegothis
Welcome to A.org - enjoy your stay :-D