Described by developer Lior Halphon as possessing the "world's most accurate Game Boy emulation core," SameBoy offers save states, rumble support, scaling filters, motion control emulation, rewind and external controller support.
"A friendly and powerful Game Boy and Game Boy Color emulator," says the emulator's App Store page. "SameBoy is a user friendly, powerful and open source Game Boy, Game Boy Color, and Super Game Boy emulator."
It's worth noting that, unlike some other emulators which have been released on iPhone and iPad lately, SameBoy does not need access to any of your personal data.
SameBoy is free to download but allows you to support its development via in-app purchases.