The only game I have is DKC, and I find it better than the original. (don't get me wrong, I love the original, but I like this better.)
Reasons:
portable
longer levels
good graphics for GBC
minigames

Zelda : Oracle of Seasons and Oracle of Ages are best!

Dragon Quest III and Dragon Quest Monsters 2 were my favorites. Absolutely amazing games.
There are many standard answers to this question but ask anyone who played DQM1 or 2 and they will tell you it comes out near the top

Pokemon Gold/Silver and Links Awakening DX

Dragon Ball Z: Legendary Super Warriors, Metal Walker and MegaMan Xtreme 1 & 2.

I thought R-Type DX was really impressive for the GBC & you had the ability to play in the original black and white.
It was the best portable R-Type game around.

http://www.youtube.com/watch?v=O4kl6_mGU_8

Wario II and 3.
Shantae.
SMBD

The one Game Boy Color game I have the fondest memories of is one I borrowed from one of my friends for a little while, Dragon Warrior Monsters. I don't even know why, since I barely remember it, but I loved it.

I loved the Zelda: Oracle games as well, despite being utterly terrible at them (as I've recently discovered is also the case with me and Link's Awakening DX ) and Pokémon Pinball.

Super Mario bros. deluxe
Links awakening dx
Shantae
Pokemon Crystal (red, blue, yellow, gold and silver are all gameboy games)
Pokemon Pinball
and so on

Oracle of Ages and Seasons (plus the link between them)

-Zelda DX
-Zelda Oracle of Ages
-Zelda Oracle of Seasons
-Super Mario Bros. Deluxe

If Gold and Silver were "gameboy games" then so were Pokemon Pinball and Links awakening DX. There were a whole bunch of games that had the extra colour of the Gameboy Color but were still compatible with the original Gameboy. I guess Nintendo gets to pick what "platform" to release it on for the 3DS VC.........

Well Mario Golf was the best version of that title on there for sure. Also little remembered but I can think of three overlooked games that pushed the GBC well and were uniquely fun for GBC unique, in a weird way. Warlocked — It's basically warcraft1 for GBC, amazingly works well using what buttons you got, talks, decent music, nice graphics, AI is ok too. Dragon's Lair — Odd yeah, but they got the laserdisc in a 4MB rom file by knocking it down to 2bit color, shaving frames off the death/rebirth scenes, removing most the music, and taking 8 'moves' away (most from Smithy.) Cannon Fodder — top down point n' click game, few soldiers, go around and shoot stuff and clear the area. That said, not-so-original wise, MGS for the GBC was quite a marvel too and I'm not even a fan of the series much, same can be said for Shantae too which is a disgustingly expensive ($100+ cart only buy on ebay so being on a download would be awesome.)