While technology is always going forward, leave it to artists to have us dream about what COULD be. Case an point: iOS on old Gamebouy hardware.
Artist BlueAmnesiac shows off what it would look like:
iOS on Gameboy by Blue Amnesiac
It's perfect! First of all it's an amazing use of the original Gameboy's limited palette and there's even a background in there.
The limited amount of screen real estate is also perfectly used, notice the little round dots at the bottom to indicate multiple screens.
In this hypothetical iOS on Gameboy, one would assume that this is a touchscreen GB but once could seriously see this as a physical gamepad only deal.
This is like the Workboy on steroids and while one could see a calendar app working on this, for something like messaging an external Gameboy keyboard would surely be needed.
The Gameboy can do a lot of things even without iOS, there's been plenty of accessories and games that tried to do things differently.
Music? Gameboy could, just see the Songpro Gameboy Mp3 Player. Camera? There's of course the Gameboy camera. Videos are a bit of a stretch but only because of space. If this thing had an SD card an a lot of compression, it could probably run videos too.
In terms of Personal Information management, there's the Austin Powers games that had some PDA functionalities.
Would this be practical? No. But insanely awesome. Ah what could have been!