I flew on United or US Airways from Phoenix to SFO with my (at the time) 12 year old yorkie, Tahoe, in a carrier under my seat. I paid like $80 each way for a special ticket for him, but it was worth not having to kennel him. I gave him a tranquilizer (only about a 10th of what they advocate) to relax him for the flight. Many people exclaimed, as we were getting off the plane, "OMG, I didn't even know you had a dog with you this whole flight!".
My Tahoe is a good boy.
~ Kelly