I have two cats.
One is a fat female cat. I have one of those soaker tubs and when I soak in it, she will sit on the back ledge and bury her head in my hair and just purr up a storm. I love that!
My male cat is very active. He has the most amazing vertical jump. He loves his feather on a stick (friend of mine once said "if only our lives could be that simple, to be motivated by a feather on a stick, to think towards the end of the work day "I cannot wait to get home to my feather on a stick"). When I am playing with him and I hold it up really high, he does Michael Jordan style jumps to get it. When he gets the feather in his mouth, he will then drag it around the house, hitting things because it is so long, but he does not care, it is his catch and he loves it.
What does your pet do that you love?