One of the easiest ways to find a new use for your mattress and keep it out of a landfill is to give it away. You'd be surprised how many people might be in the market for a free mattress. Speak with your friends, coworkers, nieces or nephews headed to college, recent graduates, or even post a message on a community board at your apartment or condo complex. The list of possible recipients is endless. Offer your free, gently used mattress in return for the new owner picking it up from your home.
If you can't think of anyone you know who might want a free mattress, you can turn to the Internet. Organizations like The Freecyle Network offer posting boards where your junk can become someone else's treasure if they just pick it up. If you're feeling generous, you may even want to have it cleaned before giving it away. However, unless you're going to sell it or give it to an organization with rules about accepting mattresses, the responsibility for having it cleaned can fall on the new owner.