My rabbits aren't "caged" but they're definitely "penned." They each have a 4x4 pen downstairs at night and in bad weather. During the day (on nice days) they each have a slightly larger (maybe 6x6?) pen to run about in outdoors. We do not let them run around in the main part of the house; Brindam finds something to hide under and doesn't budge, and while Wendy would probably like roaming the house, we don't have a very "rabbit proof" home considering several dangerous pets, too much stuff to hide under, and a lot of electrical wire. She does occasionally get to dash around in the kitchen, but honestly she seems to prefer the outdoor area where she can graze, dig, observe her surroundings, etc.
My boyfriend built his rabbits their own room downstairs, 10x7, and I bet my buns are jealous!