I used to collect caterpillars and the put them in a cage when I was younger, and my family raised sheep, and one of the sheep acted like a dog, very sweet.
More recently my husband collected 5 different snakes, 4 ball pythons, and one corn snake. He was obsessed with having different colors of them. We had a standard, an ivory, a silver, and a piebald. I was stuck feeding them and they kept bitting me so he's getting rid of all of them. One left though... anyone want a piebald ball python? That thing gives me the creeps!
I haven't had that many weird "pets". I've raised possums, squirrels, and coons, but always for release so we couldn't get too friendly with them. As far as actual pets, the weirdest I've had are still pretty common. I had 6 ferrets once. I also used to have a Jackson's Chameleon named Groovy Dude. I had an Eastern Cornsnake for a while. And I had a llama for 14 years that was spectacular - he was trained to ride just like a horse (though obviously only small people could ride him) and he would lay down and stand up underneath you to mount.
My mom had some weird ones while I was growing up though! She had a pet crow, very stinky thing! And she had a river otter for 13 years, she was devastated when he died of old age. I was really young, I barely remember him but have seen lots of old pictures and old home movies.