Donate your books to the University at Buffalo Health Sciences Library. This is a great program that's always in need of textbooks in the health and medical fields, and you can learn how to make donations on its website.
Donate to the Books Without Borders program via the UCLA Medical Alumni Association. This group brings donated medical books to Afghanistan and Iraq.
Contact the local library in your area and ask if it's in need of any used medical textbooks. Most libraries can always use extra books to add to their collection. Libraries often need to know the date of each book's publication and the book's condition, so have this information available.
Contact some local schools and check if they're in need of any of your books. Science teachers will often be able to put your donations to good use in the classroom.
Donate your books to a local thrift store like Goodwill or the Salvation Army. Typically, thrift stores will accept most donations as long as they're in decent condition.
Ask your friends, family and coworkers if they can use any of your old medical textbooks. They might have a need, or they might know of someone who does.
Place an ad in the free section of an online ad website or in your local classified ads, naming the books you have available. This is an efficient donation method because people will actually come to you for the books.