Theoretically, is it possible to run iOS on a device that doesn't ship with it? I know that Apple signed iOS so it only runs on Apple devices, but is there any hack that could potentially change that?
Theoretically? Sure, but it'd be a challenge, and I don't think anyone's done it.
However, you can sort of get it running on a Mac if you have Xcode: Xcode menu > Open Developer Tool > iOS Simulator. This will load a simulator for the iPhone with Photos, Contacts, Settings, Game Center, Maps, Newsstand, Passbook, and Safari. No way to install apps (other than making them yourself in Xcode).