I do! I hike with my son, who's now 13 and it's something I really, really treasure. He's a natural on the trail and I don't think of it as me "taking" him anymore. We're really hiking partners. He carries his full share and we carry about the same weight. Logical since we're about the same size.
My son's a pretty typical teen, involved with sports, music, friends, girls, etc. but he's still really enthusiastic about our backpacking trips. His teachers tell me that he "brags" about backpacking with his mom, which I think is kind of cool. I mean, what teenage boy brags about doing something with his mom? :) I don't know if his attitude will change in the next few years -- I'm trying to be prepared if it does -- but I hope not.
Kat, I think it's great that you hike with your daughter! None of my women friends backpack. I might talk them into camping, but only with the promise of flush toilets and showers...