Our dog is getting a little old to go backpacking anymore. Last time we wen't, I thought I would have to carry her the last few miles (she's about 40lbs).
We usually keep her on her leash when we're on busy trails, like the ones along I90 and 2. Other hikers appreciate it and she doen't mind. When we take her off leash she sticks close to us, she has some sheep dog in her and she likes to make sure her flock is ok. Kevin likes to have his dog wear a dog backpack when they are hiking, he says that other hikers have a better reaction to the dog when he has a backpack on. "Oh, how cute" rather than "your dog is big a scary"
We take our dog to the crags, but not if we're going to do multi-pitch climbs. She wants to be around people and when we leave her she wimpers and barks which is anoying to us and anyone in earshot. I've read an account of a cougar being seen at the base of static point, sniffing around climbers backpacks when the climbers are a few pitches up. Also, I've heard stories of coyotees drawing dogs away from their owners and then killing and eating them.
When I was a kid and we went backpacking/camping the dog always slept outside. Lisa makes me let the dog in the tent at night. I once made the dog sleep in the vestabule, and in the morning her nose was swolen up from being bitten by misquitos all night. I felt terrable.