Seen a little dog carrier strapped to a tour pack for a yapper also seen a medium sized dog sitting on the back seat of a goldwing don't know if the dog on the goldwing was tied on the bike some how. I have a lab that loves to ride on the wheeler but don't think it would work so well on the bike.
I ride with www.rftw.org - past two years... several people on that ride have their dogs. I am amazed at how well they ride - I only wish I could have trained my kids that well.
Funny that this just came up...here in NJ a rider was just arrested for animal cruelty for riding with his put "in his lap". Apparently someone who has seen this guy before says that he has his pug securely mounted to the tank with some sort of contraption. Friggin ridiculous to charge the guy if you ask me but that is how the local ASPCA chief operates. Oh and FWIW, the dog was not injured in any way, the guy was just spotted and stopped after someone reported him.