Do you know "Chiptune David"? There is a good chance you don´t, and I won´t blame you for that. Anyway, he is a pretty good musician and knows how to fiddle with the Game Boy as a synthesizer. I should put "was", not "is", as he has stopped making music for causes unknown to me. This track is the most well-known of his, named "Ultima Weapon".
By the way, making music on a Game Boy seems pretty hard - you need a special cartridge to allow you to program the system´s sound chip. There are several on the market, the most prominent being "Nanoloop" and "Pixelh8". Plus. there are also special modifications for Game Boys for better sound quality.If you´re interested in this kind of thing, I can recommend the Wikipedia article at http://en.wikipedia.org/wiki/Game_Boy_music .
The Game Boy is still going strong in the chiptune scene, there are lots of artists out there using it, especially for live performances. For now, enjoy this video of "Ultima Weapon" - I certainly do.