Almost all of us have at least 1 way to play most PCE games on original hardware, but that doesn't mean emulation isn't still useful. So maybe it's time we collected our observations about the accuracy of various emulators and helped flesh out which ones are the most useful. My thoughts are below. I have not tested rigorously at all, so these are rather generalized. If you have more specific information, I would love to make a list that reflects communal knowledge instead of my own (mis?)perceptions.
I know Mednafen has the greatest accuracy, but it is the least friendly to use, and many won't touch it because of the command line.
I'm a big fan of Ootake. It's free and open source and is pretty accurate, though certainly not perfect.
I do not like Magic Engine, because not only is it closed source, the author charges money, and of the current, still-maintained emulators it has slightly lower accuracy than Ootake. It seems silly to charge money for an emulator that can't best the current free options.
BizHawk is the emulator I'm watching for the future. It uses the Mednafen core for PCE emulation, though it does sometimes pick up bugs not present in Mednafen due to it being designed specifically for the TAS crowd. The developers are pretty good about squashing bugs as they come up, though.