I've recently been playing Breath of Fire 3 and 4 lately, and I'm really starting to get fed up with some of these stupid mini-games. Breath of Fire 3 is particularly bad for the amount of sub quests it forces you to run, mostly to disguise how small the game world actually is. The shisu making quest springs immediately to mind.
Breath of Fire 4 doesn't have the silly sub quests, but compensates by tossing in a ton of mini-games for you to play. Need information? Gotta play the "bribe the old man" mini-game! Want to get a ride across the desert? You need to play the "load the ship game"!
All the Breath of Fire games feature the awful fishing mini-games, though I personally feel that the version in BoF 3 is the worst. I'd skip fishing entirely if it wasn't required to get one of the masters.
Are there any other games (not necessarily RPGs) that have annoying or pointless mini-games?