Well, I didn't ALWAYS get them lol, but you can have a LOT of chickens haha. And rabbits. I actually had a room with aquairums on the wall and some pet cages, as I was animal mad was the only child at home, and was home schooled so the 'animals' also got to be a part of my education.
I used to breed guinea pigs, hamsters, all sorts of tropical fish. I did bunnies a few times (and sell the children to friends and it'd be a lesson in economy, and taking the money to put back into my 'animal room')
I even once had a pet duck that followed me about like a duck and went with us in the Summer to a lake house haha, he'd swim around with me and was Terrified of Real ducks, never knew what they were.
I've had a lot of pets in my life. And the amount of lizards, spiders, baby birds, I'd have in my pockets at any given time was always interesting as well.
When we'd go to Florida I'd always catch the cute lizards (they sold them in petshops in the north where lived most of the time) we called them chameleons but they weren't really.
The only animal I never really had as a pet was snakes. I was never scared of them, but just never felt 'friendly' enough to keep as a pet.
Had turtles and tortoises. I also used to collect frog spawn from the ponds in Spring and hatch them out and keep a couple to 'full frog' in my animal room and let em go in Autumn.
Sounds like an awesome childhood XD