While the MAME emulator itself is legal, the ROMs (the games) are copyrighted property. Distributing or downloading them without owning the original arcade board is generally considered copyright infringement.
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Seek out reliable archive repositories that specialize in digital preservation. Look for collections labeled explicitly with the MAME release version (e.g., "MAME 0.262 Reference Set"). Mame Roms Pack Download
MAME updates every month. Always match your ROM pack to your emulator version. Using a MAME 0.250 ROM pack with MAME 0.270 will result in errors. Check the "MAME version" in the pack filename. While the MAME emulator itself is legal, the