I got a gameboy, and since I’m an old fart I need to ask…
What are some good gameboy games?
My favorite has always been Quix, but then, I’m an old fart too. 
It all depends on what interests you.
However my Mom (a fellow “old fart”) was seriously addicted to “Tetris” on my GameBoy.
The complete Final Fantasy series & Zelda series & Pokemon series.
Can’t beat Tetris or the new Tetris DX (which is just a color upgrade for the most part).
If it’s a GameBoy Color, the new Tomb Raider is pretty snazzy (and Laura still jiggles when she runs, neat trick with a 1/4" sprite). Plenty of space to explore and clever puzzles.
The Perfect Dark game is good too and has a nifty “rumble” cartridge.
Avoid “Logic” at all cost though!
I’m a huge fan of “move the thread to IMHO,” but I think that’s more of an on-line thing.
My cat knocked my gameboy into the toilet last night and ruined it. I only had one game, Pac Man, but it actually had a second game on it, a tetris like game that I enjoyed more than the Pac Man game.
Now with the holidays I am too poor to go buy another one. 
I am seriously depressed over this.
Michi
Tetris Attacks, which is a version of the old Tetris, is a pretty addictive game. I would recommend buying it. Also, IMHO, look for GB games in those second hand video games stores. You’ll save a bunch of money on great titles.
Tetris and Mario.
I’m hooked on Shanghai, although the Final Fantasy series is good.
My hubby gave me a Color Game Boy two years ago for Valentine’s Day. He rocks. smooch