Free mattresses can sometimes be acquired from hotels and on classified ad websites, such as Craigslist.org. Free mattresses may have problems or be infested with bed bugs.
Many high-end hotels will give away mattresses for free when they are replaced. Ask hotel management when they are replacing mattresses and if they give them away. Remember to check for stains and bed bugs, even at high-end hotels.
Mattresses are also sometimes listed in the free category on classified ad websites, such as Craigslist.org. Be extremely careful, and thoroughly check mattresses for bugs and stains, especially in the seams. Listings are more common near the beginning and end of months, when people generally move apartments.