Trust me, this page would not be here if people that got to this site were looking for Super Mario emulators. I'm not going to advertise any here, but I will make some reccomendations to you.

For the NES...
I reccomend VirtuaNES. It's a Japanese emulator rarely heard of. I've operated it with no problem at all. A simple and easy to use emulator that can be played by anyone.
NESticle is probably the most famous NES emulators, but it's becoming outdated. It's still not bad, but newer emulators are beginning to take its place.

For the GBA...
BoycottAdvance maybe one of the most advertised GBA emulators, but it's not the best. I downloaded it and experienced many bugs and other problems with the ROMs. There are several other good GBA emulators, so search around.

For SNES...
ZSNES has been, and probably will continue to be, the best SNES emulator out there. From what I can tell, it works pretty flawlessly. ZSNES is your best bet for a good SNES emulator.

ROMs are pretty easy to find. There are several websites with ROM directories, making searching for any ROM simple. ROMs are .zip files, so downloads are quick and easy.

Please note, ROMs are illegal if you do not own the game you have downloaded.