Generally, downloading ROMs for games you do not own is illegal copyright infringement.
Top choices for mobile emulation on iOS and Android devices. Legal and Safety Reminders
When searching for SNES ROMs, you will typically want to look for complete collections or "packs." Here are top-rated search avenues: Verified No-Intro Sets
This is the elephant in the room.
While Archive.org is significantly safer than standard ROM websites, users should still practice good digital hygiene:
If you are looking to download the essentials, search for these titles on the platform: Super Mario World The Legend of Zelda: A Link to the Past Chrono Trigger Super Metroid Donkey Kong Country
Most SNES ROM pages on Archive.org have a sidebar on the right. You will see two options: