Great thread, I have a lot of appreciation for the Gameboy line and a lot of fond memories. I always loved the idea that developers had to work around the hardware limitations to bring console-esque experiences into the portable realm, especially towards the end of the Gameboy Color's life. Metal Gear Solid for example, took cues from the contemporary Playstation game, as well as its NES/MSX forebears. It was a smart hybrid, and despite not being a fan of the Metal Gear series in general, I think the Gameboy Color iteration distils all the series’ purest game play elements in a wonderfully simple way. Similarly, Link's Awakening stands out to me as being the perfect Zelda game. The pacing and difficulty curve is perfect, there is no fat in the game, no superfluous cut scenes, and it has a succinct and emotionally resonant storyline. The graphics, while primitive, are full of personality and allow you to build the world in your imagination.
Gameboy Color games resembled NES games, just with modern design principles in mind. The fact that games were actively being made for it in the 3D era meant it held a unique position in the overall landscape, especially when it appropriated console IPs and licenses. The popularity and longevity of the systems, stretching back to the original Gameboy, also meant that they amassed an enviably large library of games over their lifetimes. Sure, there was a good deal of low quality software too, but the best games, as I’ve mentioned, felt contemporary, rich in content, and as value for money as anything on a console.
In addition to the titles already mentioned in this thread, here are a couple more to throw into the mix:
Cannon Fodder
http://www.youtube.com/watch?v=BT_Gk87JdK8&feature=results_video&playnext=1&list=PLDB6460601320E36D
Astonishingly, this game has an FMV intro and a 3D menu. Great port of the Amiga classic, with a simple interface disguising deceptively deep game play mechanics.
Perfect Dark
http://www.youtube.com/watch?v=2eg_My7nYAU
Rare's interesting portable version of the N64 game. The game had a real feeling of prestige and quality, and the giant cartridge even had a rumble pak. Despite a mixed reception, due to the poor AI and sometimes high difficulty, it’s still an impressive game for the system. Came out around the same time as Metal Gear Solid, and is reminiscent in some ways.