Are you done using it? Give it away. Here are some places that will take relatively unusual items.
Bedding, including box springs and mattresses: Ann Arbor Kiwanis
Clothing, shoes, accessories, small appliances, housewares, books: Ann Arbor Thrift Shop
Clothing, stained or torn: Various donation boxes around town
Furniture, even in mild disrepair: ShareHouse on Jackson Road
Note: The Recycle Ann Arbor website also includes a list of locations for reuse, recycling or disposal.
Sources:
Facebook page from Mary Morgan
Donation Bin Locations: Donate clean, bagged, clothing and shoes to a variety of local non-profits.