I don't know if this is all that rare, but I've only ever seen one in the wild and I bought it:
Watara's Supervision was a perfect Gameboy imitator. down to the specifications of the screen. It can even use the same power supply, and on the right side there's a DB-9 port for console linking. Of course, the games were terrible and there was nothing from third-parties or licensees to make it appealing outside of Asia.
I used to own one of the Sony CD-i units, which had a built-in controller, LCD screen and ran off a camcorder battery. I foolishly sold it years ago, but it was easily the rarest (and most useless) piece of gaming equipment I've ever owned.
Yes, that's an NES Power Pad that the Supervision is lying on. That's not particularly rare either.