My older cat will ostentatiously stand guard over our baby. If the nursery door is closed with the baby in there, cat will sit outside and snarl at anyone trying to come in who isn’t my wife or I. She also eats duct tape if it’s anywhere she can find it or pry it up–I can’t use it for home repair tasks anymore.
Oh, yeah! Ponch loves my freshly-washed hair, and will make every effort to suck the water out of it! 
With Ponch, it’s my feet. If I’m sitting in the living room with my feet up (and no socks or shoes on), he will come and lick my toes endlessly. I call it getting a ‘pet-icure’. 
The tiny terrors will leave my unclad feet alone, but they are terrified of socks and/or slippers. The bat at my hands when I am putting socks on, and will stalk and attack my feet if I am walking around with either socks or slippers. When I remove my socks, they will try to steal them.
For the first 6 years of his life, my fierce male Himalayan “Fuzzy” carried a stuffed chipmunk beanie baby around as his “kitten”. Upstairs at bedtime, downstairs in the morning. Just like clockwork. We’d hear him meowing with it in his mouth, sort of a muffled “MROWFF”, and here would come Fuzzy with the chipmunk in his mouth. He’d bite it carefully behind the ears to carry it, and he was very uncomfortable when other people picked up his “baby”.
Eventually the chipmunk got lost, or else Fuzzy hid it somewhere.
My old man cat, 16 year old Noodle, has a “woobie.” it’s an old refillable catnip toy he’s had since 2002. It’s toted about in the same manner a couple times a day, when he takes it to his next sleeping area, always accompanied by muffled yowling. He’s had that thing for so long, and the other cats leave it alone. I think I’ll know something’s seriously wrong if he ever stops bringing it to bed.
One of my cats liked to get his butt sprayed with water. He hates water anywhere else though. When I like to have some fun, all I had to do was make sure that he saw me pick up the spray bottle. He would then come to me and turn around with his butt facing me and would wait for me to hit it with a couple of sprays. He would then trot away and lick the water off his butt and then come back. Rinse, lather repeat.
He would also stuff his head into paper bags that were the exact size of his head and walk blind until he hit a wall or something. Then he would shake and paw at the bag until he got it off, look around, get his bearings and then stick his head into the bag again. Rinse, lather, repeat until the bag became unwearable.
Man some of these cats sound like cash registers.
Our older cat has a thing about q-tips. Specifically, the used ones. She chews them obsessively, and nothing will dissuade her. I don’t know what’s up with that, but she’s done it ever since we got her.
The Cookie Monster does that too. But it goes further: she is in love with an old laptop bag, and no matter where I lay it, she follows. To test her, I’ve been taking the laptop out and draping the bag on weird places at strange angles, and she will still seek it out and loll all over it (she’s a lollcat).
Other idiosyncrasies: she’s jealous of laptops. When I’m working at home, the moment I’m working on a laptop, she will quack and demand attention, and crawl all over me and around the computer - I have inadvertently taught her over the years that the keyboard is verboten. Worse, though, over the past three years she has sprayed disgusting stinking musk on four of them, which is an absolute bitch to remove from a keyboard, and is particularly embarrassing when I have to bring it into work the next day.
She’s also jealous of my girlfriend, and when we’re snuggling on the sofa, she’ll climb up and plonk herself in between us. She’s not an insubstantial cat, either, which tends to break up the smooching.
Ah yessss…the petty jealousies. I remember those now.
My cats would get jealous if I brushed my own hair. Don’t think about it too hard, you’ll make your brain hurt.
Emmy likes q-tips as well, but she plays with clean ones. I haven’t given her any used ones, but if I put my finger in my ear and offer it to her, she will obsessively lick it. She also used to clean out Towelfish’s ears back when Towelfish let her bathe her. When Towelfish was a kitten, she would occasionally stick her tongue in my ear while I slept.
Emmy and I have conversations, too. We talk about her day and how she’s all alone with the Boy (LOUNE) while I’m in the office working.
Towelfish likes to roll around on the floor and squeak when she wants food. In addition to rolling, she’ll lay on her back and propel herself forward using her back claws. Sometimes she’ll do it when she already has food. Oh, and she likes to eat marshmallows. Emmy loves walnuts, but if you give her one, she just licks it and then begs for another one.
Another weird thing about Emmy is that she flees in terror if we’re walking or standing near her, but if we’re sitting or laying down, she’s very affectionate. Bedtime is also known as Stripey Time because she’ll get on the bed and start headbutting us, or she’ll lay on my chest and knead my neck.