I thought this day would never come, but today MAME -- the Multiple Arcade Machine Emulator that would let you play retro games -- is available for free in the iOS app store. Not only that, but it's compatible with iCade.
My life is now complete.
Of course, MAME doesn't come with any retro game. That would be illegal. And this app is completely illegal. There's no reason to ban it (Apple, please take note and don't remove this app from the store).
If you want retro games, you will have to download those and copy them to your iPad or iPhone using an utility that allows you to browse the file system, like Phoneview. It's easy, just locate your favourite game, select iMame in iPhone view, drag and drop the zipped ROM file into the iMame documents folder. No jailbreaking required.
If you have an iCade, this will turn your iPad into an arcade mini-me, complete with hardcore ball joystick and buttons. It's a joy to play on this thing.
It works perfectly. Now, excuse me when I go back to play Burger Time.