Your device needs to be jailbroken. There are several emulators in Cydia, including MAME, NES, GameBoy, Genesis/MegaDrive, etc.
For more info on jailbreaking, please see our hacking section. Our stickies in there will let you know whether your device and version of IOS is capable of being JB at the moment, and from there you can start exploring emulators.
There was also a legal MAME app in the App Store until recently, but I'm pretty sure it's been pulled now.
Also, please note our rules which are linked in my Sig. Discussion of emulators is perfectly acceptable on these forums, however you may NOT discuss sourcing ROMS for those emulators on here. Legal ROMS do exist for most emulators and can typically be found using Google
Hope that helps.