My cat came to me via my brother and his wife. They have always had several cats in their home and adopted what turned out to be a pregnant stray that her sister had found. We live next door to my brother and my then 7 year old son would go over every day to see the kittens after they were born. I'd had outdoor cats before, but never really wanted an indoor cat. Well, somehow I got talked into this little lady and became the parent of an indoor-only cat. [We live on a busy road and had had a couple of outdoor cats hit/killed by cars ] What ended up happening, of course, is that this cat became MY buddy. She liked the other members of the family just fine, but she took to me the most. And over the 14 years I've had her she's been a fabulous friend.
I also have an apple head Siamese that came with my husband when we married last year and she's a sweetheart as well....more cuddly than mine and full of curiosity for exploring small spaces in our home. She likes to sleep on my pillow at night.
Regarding pets that choose you, rather than the other way around....we had two cats do that....one was another tortoise-shell calico we had when my kids were little, what a sweetheart! She just showed up out back one day and we started feeding her. She wasn't in our lives too long, though. I also had a grey tiger show up one day and that little guy was a sweetheart too. Somehow he always knew when I needed a little extra affection and would seek me out.