When I was very small we had a huge (to me) rabbit kept in the hutch in the backyard. I only remember the fact that she was very big (in the eyes of a three-year-old). I never handled her and was somewhat wary of her teeth.
When my daughter was in elementary school, she had a variety of pets; one of which was a dwarf rabbit with soft tan fur. She named the rabbit Bun after her favorite stuffed toy. Bun was often let out of the cage and even taken outside, on a special halter leash, to hop around the backyard. She was a delightful addition to the menagerie and much more conducive to holding than the fish and garter snakes.