An unofficial port of the MAME arcade emulator is up on the App Store right now, for free. iMame comes with a selection of legal demo ROMs, but if you can find a way to get your own MAME ROMs onto your iPhone (Gadget Lab suggests an app called PhoneView), you can play genuine arcade games on your phone. The app even supports the iCade controller, so iPad owners don't have to use the miserable-looking touch controls.
Oh, by the way: please only use legally acquired ROMs with this program.
Apple has taken a dim view of emulators in the past, but seems to have calmed down in that regard, allowing programs like the Turbografx-16 GameBox, C64, and Capcom Arcade to live on the App Store. Still, just to be safe, we suggest grabbing this nowish if you want it.