Emulation itself is legal: writing and running emulators is protected software development. Downloading ROMs of games you do not own is generally not legal, because the games are still under copyright. The safest approach is ripping ROMs from your own cartridges or discs, and buying official re-releases where available. Copyright law varies by country, so this is general guidance, not legal advice.
Is emulating retro games legal?
Emulation is legal; downloading ROMs you do not own is not. Here is the honest breakdown.
