The closest I've had to a non-traditional pet was my two rabbits, Thumper and Flower. They were awesome to cuddle and play with. The only problem is that they were very clever. One summer, my mom bought a strawberry plant for us to have strawberries to eat, since they're expensive. She put them on top of the patio table to keep them away from the rabbits. But those brats figured a way onto the table and ate the strawberries, the leaves, the stems, and part of the roots. Other than ransacking the garden from time to time, they were a great first pet for little kids because they're not aggressive and easy to play with.
During the summer, my grandparents let the grandkids help take care of abandoned calves, sheep, and frogs. The frogs were kind of pet like because we would watch them and feed them, but they usually left their bowls as soon as they got their legs. And while we hand fed the calves but that was about it. We got to help feed the sheep but they wouldn't let us near them, so I don't really consider them pets even though we helped take care of them.