Quite a few times I’ve rescued animals and had them refuse to leave afterward, especially birds and lizards.
One of the funniest was a Western Fence Lizard I found in a swimming pool. I pulled it out and let it sit on the back of one of my fingers. We were having some wine and grilling some food. About an hour and and a half later it was time to go inside to eat and the lizard was still on my finger. I took it over to a low bush so it could get off. It didn’t move. I tried gently scraping it off on one of the branches and flattened its belly to my finger and grabbed on tight. I got a twig between the lizard and my finger and it just crawled over the twig and back onto my finger. Took me a long time to get it to stop hanging onto my finger.
I’ve had deer come up to try to lick salt off of my face when I’m sleeping, young skunks wander over to check out my shoes and watch what I’m doing, curious pufferfish decide they’re going to chaperone me around the reef on a dive, chipmunks decide that in my lap or on my trousers was a safe place to sit and watch what’s going on, etc.
I used to have butterflies land on me pretty often, but that hasn’t happened for a while.
One of my favorite experiences was on a short hike in the hills in Southern California. I stopped to sit in the shade for a bit where there was a little breeze, and a few minutes after I did a pair of foxes came out of the bushes and sat down about an arm’s reach from me. They didn’t move when I took a drink of water, and we sat together for maybe 5 minutes, after which they got up, and trotted away, with one of them giving me a quick look as though it was saying, “Take care, see you later.”