GBA4iOS 2.0 which has been updated to work with iOS 7, will let you play Gameboy, Gameboy Color and Gamboy Advance ROMS on your non-jailbroken device. There is only a slight work-around to install it on the iPhone or iPad since Apple's AppStore doesn't allow any game emulators.
All you have to do to install it is set your iOS device clock to before February 19 2014, visit the download page from your device and click on the Download GBA4iOS 2.0 button there and install. After you've run the app once, you can set back the date to the actual date. But in case you reset the iPhone or iPad, you'll have the set back the date again to before February 19 prior to the first launch of the app.
You'll be able to load ROMS either through the built-in browser of the gameboy emulator app or you can sync the ROMS from your Dropbox folder named "GBA4iOS 2" in the Apps folder. The folder is supposed to be created automatically when you switch on the sync with Dropbox in the GBA4iOS settings, however there seems to be an error authorizing the app when I tried. Perhaps this will be remedied in a future update.
The emulator even supports MfI external game controllers so if you are proud owner of a Logitech Powershell bluetooth/battery pack iPhone game controller, then you'll probably enjoy the nostalgia gaming even more.