The Mastermune Sidequest in Chrono Cross was fun as it was challenging.
High risk, high reward; the damned sword made the rest of the game too easy! x)
Breath of Fire fishing is always wonderful. I actually enjoy fishing myself, so...
Talking to dogs in Tales of Symphonia. Not a real sidequest, but dogs are great....so....
Tales of Graces had this thing with three siblings. I loved the running gag where the woman's chef kept getting taller. But I'm a sucker for running gags....SOO....
Yeah, I'm not giving real answers.
Wild Arms 3: Super bosses, alien tower bosses, books, millennium puzzle solutions, and fighting dirty magazines. Plus a 100 floor dungeon (that I never attempted because life).
Tales games in general. Though sometimes obnoxiously so with the weird cut offs and dubious rewards. But I admire that most of them are an effort at character/world building nonetheless.
As mush as I hate about 70% of the "sidequest content", FFX's adventure for the sigils were pretty varied and interesting (opposite of FF13 which gives you f*** all to do).
Baten Kaitos Origins. I thought collecting a "clay village" was cool and weird. I also liked Pacman as an odd nostalgic throwback. It was a pain in the ass, but the rewards were great. The first game also was great for unique "character quests" to tie up loose ends and given you ballin endgame equips.
Zelda games do these pretty well too. Majora's Mask is practically one giant sidequest with your major locations at each of the outer reaches of the map. Chrono Trigger too, technically.
Chocobo Hot/Cold was painfully addictive. Goes up a grade probably just for cool music.
Dumb as it is, Score Pieces in Eternal Sonata were a fantastic idea since they allowed more than one combination.
Does end/post-game Tri-Ace stuff content??? Cave of Tribulations/Ordeals, Seraphic Gate, Sphere 211, the weird-ass distotion corrdidor, Neverland.... I love post-game content to throw a knife in your back when you think you've done well for yourself.