Can I say an entire game based around a mundane task? Because at first I was hesitant to buy Euro Truck Simulator 2...but I don't regret it at all. (It does help it was on sale though on steam..) I don't know why, but I REALLY enjoy playing it. Essentially, it's just driving a big truck, but it's kinda like a racing game as well, since you have to make deliveries as quick as possible to get more cash and experience. I guess it's the sense of progression that appeals to me the most, but hey, I'm not complaining if I enjoy it. I'm actually planning on buying a racing wheel for my PC for this game (well, all my other racing games as well like GRID and GRID 2.)
As for the mundane tasks in games not strictly based around them?...I guess the social aspects of Persona 3 and 4. You know, going to high school, trying to have high scores, keeping up with all the relationships, after school activities. Sadly, I think it's because that's the type of stuff I didn't really get to experience with high school. None of my friends were really...active? I wasn't exactly the most popular. But otherwise it's because I found the side characters in the game so interesting at times. You could say I liked it more than the combat parts of the game entirely.
EDIT: Actually, I think that's not a good example either, since building the relationships and going to school can actually have a large impact on the game...hmm...another example? I guess that would be trading and getting as much money as I can in games like Fallout and Elder Scrolls. I even did an entire playthrough of Fallout New Vegas where I roleplayed as a Caravan, searching for supplies and selling them while getting my bartering skills up.