A while back, I introduced Daphne to the dog. They became fast friends, and Daphne learned quickly that he was a good candidate for riding.
When she is feeling in a really good mood, she heads over to the dog and sits on him and gives him a hug. He doesn't mind. In fact, I think that he really likes the attention.
We now have a cat in the house, and Daphne is determined to treat her the same way. She tries to sit and lay on the cat, and it is just funny to see the reaction she gets. The cat does NOT like the idea of being sat on AT ALL, so she hisses and growls at Daphne. Luckily, we have a very understanding cat, and no injuries to the baby have occurred, but I think it is pretty funny that she feels compelled to ride the cat.
As an additional note, Jared found Daphne in bed with the cat last night. She was just laying there hugging it. Despite the fact that the cat hated it, Daphne was the happiest baby in the whole world.