We have a cat, a half giant bunny, a budgie and an ever changing line up of hamsters (big and small). The only creature that was actively chosen and purchased was the budgie!
About 6 years ago we moved into a temporary rental while waiting on builders finishing our home now. There was a cat living in the bush outside, it turned out it had been a previous residents who had left it behind, we do know this. It took him a few months to come round to knowing we were "safe" and then when we moved he came with us.
Then someone in a local village posted she was getting rid of her hamster because she was allegedly moving somewhere that wouldn't accept pets. That was the first one and we've had a rainbow of different ones since and generally all the same story "bought for kid who doesn't spend time with it, it bites, it's gone if no-one else wants it". Even my little Elvi who had a major attitude problem when she first came (biting kicking screaming!) Has become a lovely little thing who let's me brush her and she will try and preen me in return. :D
Then we get onto the rabbit. We met a lady who had gone through a rough patch with her health and was left with various physical deficiencies. As a result she was moving to a kitted out bungalow, her charming partner left her that and as soon as he did the rabbit stopped being looked after. I didn't even know it existed the first few times I met her at her home despite it being in a vivarium (!) in the corner. For whatever reasons she wasn't being looked after properly, the viv was constantly shut up because of the dog, the lady couldn't get down to clean/feed her. Someone was supposed to be collecting her who had existing house bunnies and then suddenly wasn't. It seems that she realised how aggressive the bunny was. Well that's where I stepped in and moved her sans vivarium into proper accommodation in our home. Ooo she really was a git - I never realised they could growl till I met her! She would kick and bite and scratch, go on the attack, snatch food bowls right back etc. She soon learned, her and the cat have a grudging respect of one another, and she gambols around the house at will.
That leaves the budgie, we had them when I was a child and I really really wanted one for my kids. So I got one! :D