So I am going to be very predictable and say that my least favorite quest is the Fade sequence in Broken Circle. I know this puts me in company with most of the fandom, but so be it. It's a structural problem, really -- the Tower itself is a linear, unescapable dungeon, so to be thrown into a second linear unescapable dungeon in the middle makes the whole thing feel much longer and more tedious. It also feels really unfair that you can't stock up for it. My first time through, we didn't realize what was coming, so I hadn't bulked up on healing potions, and my warrior Cousland died a lot. Normally I like dungeons with a puzzle aspect, but this particular one didn't appeal to me as much. About the only thing it has going for it are the character moments in their individual nightmares -- Alistair's, in particular, I found very telling, and Sten's as well -- but because I always do Broken Circle very early in the game, I'm limited as to which characters can participate. If only I could play on PC and install the "Skip the Fade" mod -- that and the Grey Warden armor are the only ones I'd be tempted to use.
Anyway, that's my answer, and I'm sticking to it.
I actually don't think I have a least favorite quest in Dragon Age 2. I don't love them all uniformly, of course, but I can't think of one I dislike above all others.