We have a cat only because it kept sneaking in our window. It was a stray that at first wouldn't go near us and would climb back out the window when it noticed we had seen it. It gradually got friendlier and friendlier. Now it is an important part of our family. It absolutely loves my 5 yr old daughter who named it Rarity after her favorite MLP, even though it's a boy.
Feed it.
Let it grow.
Ride it into battle.