My cat Remington likes to sing all the time, and give hugs, grab asses, be held like a baby, rattle doorknobs in the middle of the night, and he fiends for Marmite Cheese sandwiches. : My cat's pretty crazy.
My dog is weird. She likes to growl at me when she wants a kiss.. Ill kiss her head then she will growl/whine at me. then pounce on me and lick my face.
My hamster, Harmony, instantly falls asleep when you rub her between the ears. It's really cute because she wakes up time to time to make sure that no one stole her food. And when you refill her bowl she jumps in it and puts all her favorite seeds in her cheek pouch, then she takes them to her igloo. She's a little paranoid. XD
My pug loves sleeping with his head on my leg/arm/shoulder/hands/feet as a pillow, and when he wants food but I don't give it to him he sits there, straightens out his tail, bows his head, and just glances up at me.
My Rottweiler mix, Khloe, hated bubbles. I found this out when he crashed into the back of our garage once when he jumped to try and pop one. Similarly, he hated balloons. He'd bark and bark and cry until someone took it away or let him pop it. He'd attack water, and was scared of the sound of the waves at the river. His favorite thing to do at the dog park was to carry his favorite orange ball around and show everyone it was his - he wouldn't let you toss it for him or anything, he just wanted to carry it around.
Lester, my snake, has an odd habit of hiding underneath his heat mat, if he can get under it (probably not quite as cute as cats under blankets...) he also tends to come and have a good look at me when I play guitar...
underneath the heat mat, under a log... how, Lester?

My rabbit, Elliot, has this bowl in his cage. Rather than eating from it, all he does is throw it around his cage.
Funny how most of the cute quirks I could think of are all the same cat.
She likes to massage my stomach. I lean backwards, clap my stomach and she jumps up and starts kneading her paws at me. It's quite nice actually.
Also she found out that when the water bowl is empty, she can get us to come pretty fast by stomping in it and dragging it on the floor. -_- She has trained us well.
My dog Luna likes to watch tv. I think her favorite movie is Kung Fu Panda. She seemed to really like that movie and had a hard time taking her eyes off the screen.
She also likes to burry pieces of her food under the blankets in MY BED! And one time I was eating a bowl of watermelon while sitting on the couch and she used her nose to move the blanket so that she could cover my watermelon. >:|
My other dog is fairly normal...except she gets scared and hides under the table or runs away every time my dad sneezes.
My 8-month-old kitten, Emma, freaks out when anyone uses the ice maker on the refrigerator. She runs into the kitchen, making her I-want-it noise and pretty much bouncing on her toes mewing until whoever made ice gives her a cube. Then she spends the next half hour smacking it around the kitchen floor until it's too melty to play with anymore. XD She also likes to watch tv, especially hockey, where she sits on the tv console and follows the puck and players all wide-eyed across the screen.
My 6-year-old cat, Holly, still makes my mom hold her every night like she did when Holly was a kitten. She'll sit at Mom's chair and whine until Mom notices her and tells her to jump. Then she'll jump and climb onto Mom's chest and curl up so Mom can hold her. Mom complains but still does it every night. XD
Oh! Kitties! I forgot about our cats' quirks. Shy Guy & Itty Bit go on "missions" together - Itty Bit leads the way, sneaking into the bathroom, followed by Shy Guy, and they steal Q-Tips and then leave them all over the house. Itty Bit also steals tampons. Tubby guards the water bowl. She's a big fat cat (if you couldn't guess) with long hair, and she lays right at the edge of the bowl so that her hair gets all in it and I have to clean the thing fifty times a day. She prefers her water from the kitchen sink, though. She'll meow and meow and meow until you turn it on for her, then she'll bat at it with her paws and drink from the faucet. We have another water bowl that the dog and the cats share. Shy Guy doesn't like if it isn't filled to the very top. If the water's too low for him, he'll stick his paw in and grab at the bowl and he manages to drag the bowl around the room - if he doesn't knock the bowl over and spill water everywhere.
My rabbit does the exact same thing.One time I was brushing him and he threw his food bowl out his hutch. I put it back in and he threw it out again. It turned into a game of "In, out".
My cats like to stick their paws under the bathroom door while I'm brushing my teeth or taking a shower. Nothing too weird, but it's still hilarious for me to turn around and see three or four paws under the door. XD
"You're always talking about X but you're thinking about Y. Learn to talk about Y, forget about X. X is going to take care of itself." ~ Grand Canyon
I donno, I guess rabbits have a global conspiracy against bowls. Or maybe they're trying to protect us from bowls because bowls are actually evil??
Either way, all I can hear in the morning is the banging and crashing of the bowl against the metal of the cage as my rabbit battles it to the death. (I think the bowl usually wins.)
My cat knows the word "kiss." :3 She'll run up to me after I come home from school, and I just say "kiss!" and she touches her nose to my lips. It's so adorable.
One of my Chinese water dragons does this thing where they try to eat the carpet. If the lizards are out of their tank with me, I have to keep close watch to make sure it doesn't eat carpet fuzz and other random things off the floor. D;
Sleep under the blankets, and she likes to curl up next to me. Between my stomach and knees (I curl up) and my butt and back of my knees.
And she's a pudgy kitty so shes warrmm O3O
My cat Percy loves feet. In the mornings, when he's particularly cuddly, he follows me into the bathroom, sits on my feet, and licks them. It's kind of creepy but pretty cute.
He also likes to fall asleep sitting up, but that might be because he's still a kitten. :P Then there's the fact that when he gives you love eyes (CAT OWNERS KNOW WHAT I'M TALKING ABOUT) he goes cross-eyed. He's pretty much the cutest thing ever.
My older cat, Boo, loves to be spanked. Like I'm not just talking about gentle spanking, he flat out likes being pummelled. Usually just on his hind quarters and his tummy. He purrs and purrs and purrs and rolls around and sticks his butt in the air. Weird little fucker.
Both my cats love to be held like babies, and they both know how to do various tricks, like sit, high five, speak, etc. Still working on the tricks, though!

If we've got our ferret out when we go to bed, she'll crawl into the bed at night and sleep between my feet. It's so sweet haha.
Her main quirk though is that she loves citrus fruit. If there's an orange or lemon on the table or something, she'll knock it off and then roll it around the room for about ten minutes. She won't eat it or anything, I think she just likes the smell!
My black Siamese is very hyper. Whenever I'm in the kitchen and open a cabinet, she'll immediately leap onto the counter and launch herself into the cupboard I just opened. She also likes to pick fights with our other cat, who is much bigger, and always kicks her ass.
My other cat is a Venus Cattrap. She will let you pet her for a few seconds, then flop over and expose her belly. The second you reach down to pet it, she grabs you with all of her paws and tries to bite your hand.
[img align=right]https://img.subeta.net/items/minion_dandybun.gif[/img]