If there was one thing I enjoy tremendously in the handheld gaming world is a nice RPG. You can find a comfy place, dig in, and work through the quest/story for a while, or, if you have only a quick moment, you can grind some XP or currency to help break the monotony of leveling or affording gear/spells.
I've played a few RPGs on Gameboy systems, including:
Final Fantasy Legend
Dragon Warrior I & II
Dragon Warior III
With the exception of Final Fantasy Legend, you could say that my portable RPG playing was reliving NES and SNES RPGs in portable form.
In any event, my favorites from that list are easily:
What RPG games on Gameboy systems are your favorites?