I'm not really into portables so I don't own very many GB/C/A games, and had even less back in the day.
I don't remember when I got the Game Boy but it couldn't have been too early on as I didn't get Tetris with it. The game I got along with it was Super Mario Land 3: Wario Land, which is a game of pure awesomity that I continued playing long after I discovered every little secret. It was a while before I bought a second game, which was Metroid 2. I played a little bit, didn't like it, and instead played through Wario Land again. Much Later I got Kirby's Dream Land, which has since mysteriously disappeared.

Despite the inhuman amount of time I've spent playing Wario Land, my favourite original Game Boy game is probably FaceBall 2000. It's too obscure for it to not be.
I still have that lovable little brick. If it weren't for it having a buildup of dirt under the screen cover, I'd probably still use it because I find it to be the most comfortable Game Boy system.