Our family has had quite a few cats since Hubby and I were married almost twenty years ago. I think we got all of the weird ones - either that or living in our house made them weird, it certainly has had that effect on the kids.

Muffin apparently had a standing appointment outside somewhere at 5:30 am. She would wake me up by chewing on my hair. Whatever it was that she needed to do outside every morning at 5:30 didn't take very long to accomplish. Five or ten minutes later she would be howling to get back in.
Squirt loved to play with mice. We were living in a house trailer on a country lot at the time, so she had lots of little mousy playmates. Squirt was a generous pet. She would bring her new friends into our bed at night so that we could play, too. We gave her to a family with an upholstery shop. I'm sure she found lots of playmates there.
Mittens had some very strange parenting tactics. When she was weaning a litter, she would get a wet dishcloth, bring it back to her kittens, drop it beside them, and leave. I have no idea what she expected the kittens to do with the dishcloth. After we gave away her kittens, she would run around the house with a dishcloth in her mouth, mewing pitifully. I felt so sad for her. We took her to the vet so she wouldn't have to go through that experience twice a year anymore. We still kept finding dishcloths under beds and couches for a while, though.

Sasha would ring the doorbell when she wanted back in. The first time she did this, I was sure that the neighbor children must have been playing a trick on me. I answered the door, and saw only our cat sitting on the step. After a few more times, the scratches on the doorframe confirmed that our doorbell ringer was definitely feline. Hubby moved the doorbell higher up, and the scratches in the doorframe got deeper.
We're down to one cat now, a six-month old freaky kitty named Arwen. She is nothing like her elf-queen namesake. She is neither ladylike nor genteel, preferring rather to run like thunder around the house, leaving cat scratches on the furniture, railings and on whomever gets used as a feline launch pad.

Now our kids are begging for a dog.