Image from MacRumors
I wouldn't anticipate this lasting long, unless we're seeing a shift in Apple's strict "no foreign executable code" policy which has been the bane of iOS users wanting to play some classic games on their device. But a MAME emulator called iMAME has snuck into the App Store and shows some great promise. It ships with a handful of classic games already installed, but using a file uploading utility for the iPhone you can load up any MAME ROMs you like (search iDOS if you need some help, same process). We've seen a number of emulators find their way into the App Store over the years and each one disappears shortly afterwards, so get it while you can.
Update: iMAME has been pulled from the App Store.