My dog loves to do stuff like that; she'll squeeze into the laundry basket, preferrabley if it is full of clean clothes..and loves to lean her head on anything hard.
My big cat does that too. We are always having "box blowouts." Though he is huge, so a Xerox box lid is still a little small for him, but he tries any empty box. If he can't get in it, he will lay on it.