This is one of those things where I can't pick just one! I love lots of animals for different reasons.
I had cats growing up and in college and we have a cat now. We also have a dog now and I love them both. The relationship with a cat is very different from with a dog and I enjoy the aspects of both types.
Then we get into wild animals! I'm fascinated by orangutans, octopuses, and crows. Though it's really any animal with above-average intelligence.