I have several cute pet stories!
Our current dog, Smokey, likes it when we have time to give him our full attention (naturally!). Usually in the mornings, I have about 5-10 minutes where I'm just sitting on the bed, drying my hair, and not really doing much. Smokes likes to demand attention during that time. He's figured out that when I stand up, attention time is over for the rest of the morning. So now, he lies on the bed in such a way that my legs/towel are trapped underneath him. When I tell him "Come on, get up", he'll instead flip onto his back and beg for tummy rubs! Anything to get more attention! I've almost been late leaving the house several times due to this, but I just can't say no to my adorable dog begging for attention!
My grandparents have a beautiful Great Pyrenees named Lady. She's usually a very sweet dog who loves all visitors to the house. About 4 years ago or so, my grandfather got very sick and was in the hospital quite a bit. When he came home, Lady got very protective of him, but we didn't realize just how protective. My DH and I went over there to visit around Christmas, and Lady was very happy to see me (she's known me since she was a puppy, after all) and was equally not happy to see my DH. She started growling at him! I tried to calm her down, telling her it was okay, he's with me, he's a friend, but she kept growling. All of a sudden, my grandfather hollers out "Lady, you b*tch! Stop that and behave!"

Lady looked very abashed at having to be yelled at, and let DH past her to go say hi. My grandfather looked at both of us and said, "Well, she is, so it's not like it's an insult or anything!". I was almost laughing too hard to hug him! Since then, Lady's nickname has become, "Lady, you b*tch!".
When I was growing up, my dad had a purebred Samoyed named Nikki. After we moved into the house we lived in now, we discovered a slight problem. The big 90 lb blinding white dog was somehow managing to disappear out of our backyard. We'd let him out, and when we went to let him back in, we couldn't find him. The backyard is just one big rectangle, so we should have been able to see him no matter where he was. One day, as I was calling for Nikki, I happened to go over to the edge of the deck and look over the railing to see if he was in the shade. I saw a pair of white paws sticking out from *under* the deck, and watched as he pulled himself out from under the deck, flat on his belly. He looked pretty silly, but appeared to be okay and happy. After he got out from the deck, I went over and peered under there. He had a nice little depression all scratched out. We didn't have AC at the time, so it was his way of keeping himself cool in the summer. Not to be outdone, my big black dog Rody found another way under the deck, under the stairs, to create his own cool depression. They both loved to be under there, curled up in the cool dirt. My parents have had several dogs in the years since Rody and Nikki died, and not one of them has shown any desire to crawl under the deck like those two did.
Last story, speaking of decks. When we first got Smokey, four years ago, we invited one of DH's friends over with his dog so the dogs could play together. Zach has a pug named Molly. Smokey and Molly had a great time playing in our yard, running up and down the yard, until Molly discovered the our deck was high enough off the ground that she could run underneath it. Smokey, being a lab/hound mix, is not small enough to fit under the deck. Cue Molly running around under the deck, while Smokey mimicked her route on top of the deck, and all of the adults stood around laughing hysterically!