Rampage 2: Universal Tour (Digital Eclipse/Midway, 1999)
It has backgrounds, building variation, and even a real plot, so it's clearly better than the World Tour port from yesterday. That said, it's still not much to look at and every level is the same thing, so it wasn't received well even in 1999.
Rampart (Digital Eclipse/Midway, 1999)
I've always loved Rampart even if no one around me does. You place cannons inside castle walls and then shoot at either incoming ships or enemy castles. After 30 seconds, you get another 30 to repair your walls with tetronimo shapes. If you surround another castle, you get more space to place cannons, but if you can't repair the walls to surround any castles, you lose. I wouldn't recommend this particular version over any of the others, but it's a great little arcade game.
Raku x Raku - Cut Shuu, Mishin, and Moji (Natsume/Jaguar, 2000)
These three aren't games, but I'm including them anyway because they're on my list. They were basically control software for Japanese sewing machines that let you make patterns on your GBC.
Rats! (Tarantula Interactive/Take 2, 1998)
You're the rat on the right and you have a gun that does absolutely nothing to the snails. I thought that meant I had to jump over them, but you can't do that either and making contact is instant death. After two attempts at that, the game froze. Quality stuff.
Rayman (Digital Eclipse/Ubisoft, 2000)
I don't know if the console version of Rayman is worth playing now, but the GBC version unfortunately is not. While more impressive than most other GBC platformers, the limitations of the system still mean it has to be fairly slow and it can't fit much of anything on screen.
Rayman 2 (Ubisoft Milan/Ubisoft, 2001)
I wish I could say this just had the same flaws as the first game, but in switching devs they apparently lost anyone who could make music for the GBC. It's the first game again, but now with terrible music.
Razor Freestyle Scooter (Crawfish Interactive/Crave Entertainment, 2001)
You might think the inspiration for this was Tony Hawk, but no, it's Paperboy. Someone seems to have decided that the right way to promote Razor was to take an ancient arcade game and zoom it way in so you can't see anything. They were wrong.