It definitely relaxes them! Sometimes when we go to events and things there will be a dog "massage therapist" there offering dog massages for a small fee or free, and I usually get the dogs one. My dog Ginger LOVED it, and once she actually fell asleep while getting a massage so I'll say she was definitely relaxed! At one event we went to, there was a man there who did them and Ginger walked right up to him and put herself basically into his arms for a massage (I actually didn't know until after she did it that he was a masseuse!) Bianca likes them too.
my mother has a boarding/grooming kennel and practices t-touch (tellington touch) on the stressed out dogs, it really seems to calm them down, it's really neat! there's different massages for different issues (barkers, nervous, etc.) and anyone can learn to do it.
I've been "massaging" my dogs for years. I just poke and prod at muscles till I find one that feels tight (you know yer dog, it's common sense) and when I find said tight muscle I work on for awhile. I had a Border Collie that would relax to the point that I wondered if it was a light coma, she would go wet noodle limp and her breathing would shallow off to an almost worrying extent. She loved it, was the only time that dog wasn't vaguely blurry due to her constant motion.
My current dog, a GSD, likes the massage okay. He prefers...well...what amounts to beating. Hard slaps and knuckle raps are his thing. Takes all kinds I suppose.