Emulation is not new on iOS devices. Despite the App Store's tough restriction, jailbreakers have enjoyed emulators like GBA4iOS and PPSSPP (PSP emulator).
Afterwards, a temporary hack permitted non-jailbroken iOS users to install apps that weren't on the App Store by changing the date of their device.
With iOS 9 allowing unsigned app, new emulators were bound to appear. Newgamepad is the latest one and it promises a huge list of consoles in one emulator.
First of all here at PG we do not condone piracy so you must have the original games if you wish to use this emulator.
Next, you should note that the emulator's interface is in Chinese but you'll be able to play your games just fine in English.
Newgamepad supports the following platforms:
NES, SNES, GB, GBC, GBA, Genesis, PSX, PS1, NDS, PSP, MAME, NEO GEO and WSC
So how do you get it?
Download the app here and then go into your settings -> general -> Profile management and trust the developer ("Fuzhou").
From there, you'll be able to download roms for different platforms.
If you can't or if the app says "forbidden", you'll have to use a VPN and set it to China. You can use either Hotspot Shield or Tunnel Bear.
This wasn't required a few days ago so it might change. Just as the app might become available in English in the future. The game's framerate will vary depending on your device's horsepower and certain games may not work at all.
Also, you can use a PC/MAC app called iExplorer to drag and drop roms directly into your device, without requiring the use of a VPN. Follow the instructions in this video.
If Newgamepad sounds too complicated, you can also try Happy Chick Game Emulator (iOS and Android compatible), which is in English and emulates the following platforms:
MAME, GBA, GBC, SNES, NES, PSP, N64, NDS, PS1 and Dreamcast.
Follow the instructions on this page to install it.
As a reminder: Here at PG we do not condone piracy so you must have the original games if you wish to use this emulator.