If you've ever read Phillip Pullmans 'His Dark Materials' you'll know what a daemon is. A daemon is your spirit (whether you believe in it or not) manifeisted outside of the body. It takes the form of a animal that is most like your personality, what do you think your daemon would be?
An example is a servant of somekind, there daemon would be a dog, very loyal, likes rewards and does what its told.
I think mine would end up being something like an owl, I'm quite clever and this animal is linked with wisdom and kindness however owls aren't exactly the boss of the animal kingdom and only fly at night, this could show my shyness...? Just think about it.