When the App Store first opened, Apple wasn't very keen on running emulators. Not only can they easily fall into a gray legal area, but allowing extra layers of code to run didn't seem safe to Apple at the time. Since then, however, Apple has loosened its policy, and now emulators of old consoles and hardware with official clearance are good to go. The TurboGrafx-16 Gamebox is one of those. It's an emulator of the old TurboGrafx-16 console, and since HudsonSoft designed it and most of the games, they're fully within their rights to sell the code on iOS. The app is free, and old school TG16 titles like Bonk's Adventure, Gradius and Bomberman '94 are available right there in the app for an in-app purchase of US$2.99 each. You also get World Sports Competition for free, so if you just want to download it and see how it works, you can do that.
A recent update to the game added five new titles, including Bonk's Revenge, Double Dungeons and Benkei Gaiden, and the controls have been tweaked a few times recently as well. Unfortunately, because it's an emulator, there aren't any iOS extras like Game Center integration, but that's not the point. You really just want to play the old TG16 titles, mostly as they were intended. Kudos to HudsonSoft for putting this all together.
Someday, maybe, when the iPhone and iPod touch have finally conquered Nintendo's handhelds like Nintendo beat Sega (no, I don't think that's going to happen any time soon, either), we can finally see a SNES or even a Nintendo 64 emulator running officially on iOS. But until then, the TurboGrafx-16 is worth a look.