The Wide Boy 64, created by Nintendo, is more or less the N64 version of the Super Game Boy, capable of acting more or less like a Game Boy Color with a TV display. It's roughly the same shape as a N64 cartridge, though twice as tall and with a slot in the top to plug in the GBC games. This is especially handy when bug testing, because you can feed the signal through a VCR and record what's going on in the game on tape, making it easier to go back and see what's going on when things go all FUBAR.
The controls are pretty much as would be expected, replacing the SELECT button with the Z trigger, and using the D-pad to control the action instead of the control stick. The A and B buttons are, of course, mapped to the corresponding buttons on the controller. The L button toggled anti-aliasing, which existed thanks to the fact that the Game Boy screen has a lower resolution than a TV screen. This was also reflected by the fact that tilting the control stick up and down allowed you to zoom the display from a full-screen view to an actual pixel-accurate size.
yerricde mentioned that these were a very rare peripheral thanks to Nintendo not setting up facilities to mass-produce them, which meant each had to be mostly hand-built. There is also a version that can play Game Boy Advance games.
The Nintendo GameCube's new Game Boy Player will essentially replace all use of these devices.