Game Boy is a fun, less expensive way to play games. I have GameBoy and Gameboy Advanced. I like non-violent, "cute" games, so that's mostly what these are.

Gameboy (original): Has many fun games, but the poor graphics make it less exciting and hard to see. Play the games on a GB Advanced if you can.
                          Original games:

Kirby's Dreamland: A very cute, simple game which has many levels. One of my favorites.
Tetris: A very basic game, but a lot of fun.
Pacman: I actually have Mrs. Pacman. It's fun but gets boring.
DK Land 2: A really fun game, but almost impossible to see on the original GB. Very challenging.
DK Land 3: A little better than DKL2.
F1 Racing: A basic racing game. Fun but simple.
Zelda- Link's Awakening: A great adventure game.
Pokemon: A great game, I love the music too.

Kirby Tilt & Tumble: A really cool level game which you control by tilting the Gameboy.
Other Pokemon games: I've never played them, but they aren't supposed to be that great.

 Gameboy Advanced: A really neat game system. Wonderful graphics, too.
                         Gameboy Advanced Games:

Warioland 4: A fun, silly level game.
MarioKart Super Circuit: A slightly worse version of the N64 game. I still love it.