According to this Yes:
Salvation Army
The Salvation Army accepts donated mattresses and will provide a receipt for tax deduction, depending on the condition of the mattress. According to the Salvation Army website, smaller mattresses in good condition provide a $35 tax credit if the mattress is in high quality condition. The tax credit can be as much as $75 for large mattresses in high quality condition. Tax credits are lower if mattresses are in poor condition, and the organization will not accept mattresses which are seriously torn or impossible to use without repair.

Shelters
Shelters for battered women, runaways and homeless people often need extra mattresses. Some shelters will accept any mattress which can be slept on, although rules vary from shelter to shelter. If there are stains or torn fabric on the mattress, you may have to repair or sterilize the mattress before donating. Some shelters will make arrangements to pick up the mattress so you won't have to deliver it.



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Really pissed me off to see all those mattresses just get thrown away. They actually paid for extra dumpsters to store them in before they were disposed of as well so it wasn't cheap. I don't know if this is Marriotts Policy or the owners of the MAYO CY, but I found this very sad and wasteful. I stayed in one of those beds in the past year at the CY mayo btw and they were in good enough condition to be used elsewhere.