My favorite RPGs have been primarily the most lighthearted ones, where typical melodrama is sparse. Some of my tops:
-Super Mario RPG
This was the first RPG that I ever loved. Very accessible and a ton of charm through which Paper Mario followed suit.
-The Paper Mario series (great level of interaction outside of battle)
Great level of interaction outside of battle.
-Grandia
It didn't live up to my expectations but I admire the fact that the game refrains from being too serious, has a colorful cast and distinct battle system.
-Metal Max series
I've only played the first on Super Famicom and the one on PS2 but the game breaks the typical JRPG mold by being post-apocalyptic/sci-fi, comical, and open-ended in one package.
-Dragon Quest VIII
I've only played a few of the games but DQ8 was my favorite. There are some dramatic moments but they were executed tastefully and not overbearing.
I haven't played the Mario & Luigi games but they look interesting so I'll keep them in mind.