When you purchase a new mattress and have it delivered, the furniture store will often pick up your old one either for free or for a minimal fee. Someone else taking care of the headache of removing the mattress is worth spending a few dollars. Not every company will do this, so find out if the service is available before buying the new one.
Online free recycling programs allow people who want to give things away connect to people who are looking for something for free. This way items are given to someone who can use them rather than being trashed. Mattresses are ideal for this since they can serve so many purposes other than just a place to sleep. Many waste facilities have special recycling programs that accept mattresses. These businesses take apart each mattress, and appropriately recycle all the different materials.
If you can't find a recycling program, many mattresses find a new home in a landfill. While this is not an environmentally responsible way to remove a mattress, it does take it off your hands. Always check with your local facility to ensure they accept mattresses before hauling it all the way out there. Otherwise, you may be confronted with an unpleasant surprise when you have to take the old mattress back home. Ask your refuse company if it provides a special pickup service.
Many homeless shelters and community donation programs are happy to accept used mattresses. Ensure that the mattress has been cleaned before giving it to one of these good causes; they don't need to deal with any bugs that might be living inside. Some fire stations accept old mattresses for use in training exercises where old buildings and furniture are burned.
During the Great Depression, many people refused to throw anything away; every single item had a new purpose once it could not perform its original purpose anymore. Follow this way of life, and take apart an old sagging mattress and repurpose it. Cloth, buttons and cotton stuffing can be used to make pillows for your pet. Non-woven lining can be used as landscaping cloth to keep weeds out of your flowerbed. Springs can be used as plant trellises, and wood from the foundation can be used to build or repair something. Cording can be used to tie garden stakes.
If all else fails and your neighborhood association allows it, put the mattress on your front curb with a free sign attached. People will gladly take anything for free. You might be surprised how quickly it is snatched up.