All of these emulators are websites that come with at least 2 platforms of ROMs and don't need you to provide your own ROMs:
game-oldies.com - NES, SNES, Game Boy, Game Boy Color, Game Boy Advance, Master System, Game Gear, Genesis/Mega Drive, SEGA 32X, SEGA CD, TurboGrafx-16/PC Engine, TurboGrafx-16 CD/PC Engine-CD, Arcade, Neo Geo, Capcom Play System 1, Capcom Play System 2, Capcom Play System 3, PlayStation 1 (the sound emulation is bad, but the graphics emulation is good), Atari Lynx, Neo Geo Pocket, Commodore Amiga (the only computer to be emulated on game-oldies.com) and Atari 7800
online-console.com - PlayStation 1, Nintendo 64, Genesis/Mega Drive, PlayStation 2, Wii, DS, GameCube and Game Boy