I'm constantly amazed at how much fun old video games are. Until now, you needed to keep you old game console running to keep playing them, which is pretty difficult. Emulators are computer programs that make your computer look like a game console. You just feed them the code from the cartridges. If you own the original cartridge it's legal to download a copy and use it in an emulator.
Now, you can play them on your phone. iEmulators.com is dedicated to apps which can run these games. Unfortunately, Apple doesn't actually allow such programs on the App Store. But, iEmulators.com found a way to get around this. An app developer can install whatever he wants on his phone. iEmulators.com provides a service called BuildStore, which basically adds you as a tester to their developer account. Very cool.
The best app to run your classic games is Provenance. I've played SNES games like Zelda and even Gameboy Advance games like Earthbound 2. These are great games, that a take weeks to finish.