GB/GBC make for an interesting case; every game I can think of that I would still download today is owned by either Nintendo or Square-Enix:
Nintendo:
Kirby's Dream Land 2, Legend of Zelda: Link's Awakening DX, Legend of Zelda: Oracle of Ages, Legend of Zelda: Oracle of Seasons, Pokemon Trading Card Game (still the greatest by far of Pokemon's dozens of spinoffs), Super Mario Bros. DX (definitive version!), Super Mario Land, Super Mario Land 2
Square-Enix:
Dragon Warrior I&II, Dragon Warrior III, Dragon Warrior Monsters II*, Final Fantasy Adventure (AKA Seiken Densetsu 1, the predecessor to Secret of Mana)
*either version; but depending on price I might just buy both because DQ is awesome and needs to be supported
And possibly Final Fantasy Legend III, which is a SaGa game. I'd have to think for a while about that one--it was kind of okay, I guess, and it did have some nice features like one of the greatest airships to ever appear in an RPG, as well as battles against like twelve enemies. FFL and FFLII, however, can burn.
On that note, I'm off to go search for Stumpokapow's list (and the responses to it,) since his reasoning is pretty much in line with mine, and used exactly the four examples I would have: Metroid 2, the Mega Mans, the Castlevanias, and the Pokemon main series. All virtually if not entirely unplayable to me by this point.