Here is the picture that gave me the idea for this weeks poll over on the right sidebar. I found it amusing and endearing, mostly because I love cats and own three. None of mine would go for this, but the biker cat seems to be up for anything.
Some people have a dog that would go anywhere the human goes. Why not a motorcycle ride?
It's probably not safe for an animal to be on a motorcycle, but if your companion wants to ride then they should be able to enjoy it with you.