cage, coop - an enclosure made or wire or metal bars in which birds or animals are kept

rabbit hutch - a hutch for rabbits

igloo, iglu - an Eskimo hut; usually built of blocks (of sod or snow) in the shape of a dome

mudhif - a reed hut in the marshlands of Iraq; rare since the marshes were drained

shelter - a structure that provides privacy and protection from danger