Alot of good titles mentioned allready but I"m gonna be picky and narrow it down to just 2 games per platform-
Regular Gameboy titles- The best one is Donkey Kong '94 bar none. It's been 10 years since this game came out and I can still whip it out and play it extensivly. Just simple to play hard to put down fun. If I had to pick another I'd say the original tetris is always a good bet, no new gimmicks just blocks composed of 4 squares that interlock to give you points.
Gameboy Color titles- Zelda Links Awakening DX, see some of you might have just put this under regular GB games but this version was improved and probaly easier to find right now, I find it's a heck of alot more fun then the capcom developed oracle games to boot. Shantae is another overlooked but prolly hard to find GBC title , it's like zelda 2/wonderboy in nature. Pretty much a side scrolling action RPG.
Gameboy Advance - This is the hardest one to narrow down to just a couple of games, there are so many great titles , most of which are snes ports to pick from. Either of the metroid titles are a safe bet but Zero mission is defenetly more fun then Fusion is. If you like castlevania but not metroid thematically then Aria of Sorrow is a nice substitute for zero mission. For RPG titles, there isn't anything better then Mario and Luigi on GBA.
So to recap in bullit form-
Metroid Zero mission OR Castlevania : aria of sorrow
Mario & Luigi super star saga
Zelda Links Awakening DX
Shantae
Donkey Kong '94
Tetris
With just these 6 games I'm sure you'll be kept busy for awhile.
