1. Sheppard "befriended" a Lantean bird a few weeks after arriving in Atlantis. It had built a nest not too far from his favorite balcony, and he loved to watch her soar while he just stood there thinking or trying figure out - or calm down from the latest crisis. Occasionally he would bring her food and leave it on one side while he moved over to the other to watch.
2. It took nearly a month, but Sheppard finally discovered that Ronon had a pet. It was a small predator and sort of looked like a kitten size-wise. The creature seemed to be perpetually stuck in the form between a small kitten and a half-grown cat; all long limbs and the kind of thin both people and animals seem to get when they're between growth spurts. Except for the part where it had a double set of very sharp teeth and equally sharp retractable claws, those where definitely full grown.
Ronon told him he had found it on world that had been recently culled. She had attached herself to him as soon as he stepped through the Gate, had slept beside him that night, and hunted and killed an animal almost twice her own size for him by the time he woke up. And when he had gone through the Ring the next morning she had followed him unhesitatingly.
Sometimes they had hunted together, other times separately, and when Ronon had to Run from either Wraith, people, or some kind of hostile animals he put her in one of his coat pockets. This was apparently where she had been when Sheppard and Lorne's teams had arrived on Planet Sunshine.
When Sheppard found out he had sighed, asked a few pointed questions and then simply told him to make sure Dr. Weir and certain other personnel didn't find out about her. This decision had been rewarded a few missions later when the cat creature chewed through the rope binding Ronon's hands together so he could free the rest of them and they could escape from their latest capture.
She kind of became the team mascot after that.
3. Sam the Pegasus Whale quickly came to be considered McKay's pet after the whole submerged Jumper incident. He was kind of fond of it, but he would rather have his cat.
4. There were a number of large aquariums in the walls of the Atlantis hallways. The biggest one was floor to ceiling and stretched across a whole corridor, there were two covering half a corridor each, and the rest were window sized or smaller.
The marines requisitioned them in collaboration with the Zoologists, and they filled them with local sea life, and various species they found in seas and lakes off-world. Dr. Beckett kept ruminating about how his turtles would probably love it in one of the tanks.
The largest one was home to a small group of Pegasus seahorses. They kind of looked like pegasi if you squinted at them sideways, including some wing-like fins. They had a lot of spectators, and seemed to enjoy the attention if their antics were anything to go by. The seahorses appeared to thrive on the attention in a way similar to dolphins, even if the various attempts to get to play with beach balls kept failing since they didn't like being above water.
5. Teyla was given an Earth kitten by Lindsey Novak in their third year. No one could quite figure out how the kitten was smuggled onto and then off the Deadalus without Colonel Caldwell noticing, but no one's complaining.
The cat lived in Teyla's quarters but she occasionally brought it with her to the Mainland so it could run free for a few days. The Athosian children loved her because she was playful and loved running around with them.
Ronon's little predator was the only one who didn't seem to like her, but she would leave her alone if there were a couple of people between her and the cat.
Rodney, of course, was insanely jealous when he found out, and even more so when Teyla wouldn't tell him who gave her the kitten so he could have his own cat smuggled onto Atlantis.