Favorite Gameboy game, huh... Well, I'll leave out Gameboy Color games then.. So, my favorites would be..
The Legend of Zelda: Link's Awakening
Metroid 2: Return of Samus
Tetris
Super Mario Land
Teenage Mutant Ninja Turtles: Fall of the Foot Clan
Those were the 5 that I played the most, out of the games that I had. I didn't have a huge library of games for the Gameboy. I was dependent upon either my parents buying me new games, or, borrowing games from friends. But these were the ones that I owned that I played the most. I had probably 20 Gameboy games in total, that I owned. But my friends had different games too, and we would borrow each others games here and there.
Link's Awakening ans Super Mario Land have some of my favorite ending music. I liked Tetris's music too. But I would beat Link's Awakening and Super Mario Land, just for the music. I once put brand new batteries into Super Mario Land, beat the game, and just let it sit and play the music, nonstop, until the batteries died, as I did my homework to the music.
Super Mario Land Ending Theme
http://www.youtube.com/watch?v=Yu7qb5ETYcY&feature=player_detailpage
The Legend of Zelda: Link's Awakening Ending Theme
http://www.youtube.com/watch?v=MtGrBQuNy8s&feature=player_detailpage