Some over-the-counter nonsteroidal anti-inflammatory medications include ibuprofen, sold as Advil or Motrin; naproxen sodium, sold as Aleve; and aspirin, sold as Bayer, Ecotrin and Ascriptin, according to WebMD. NSAIDs work by blocking the bodily production of chemicals that cause inflammation.
Useful for treating conditions like tendinitis and arthritis as well as long-term pain, some NSAIDs are only available by prescription, notes WebMD. These include celecoxib, sold under the brand name Celebrex; prescription-strength naproxen sodium, sold under the brand name Anaprox; and diflunisal, sold as Dolobid. Prescription-strength ibuprofen is also available. Regardless of whether an NSAID medication is purchased over the counter or by prescription, NSAIDs may increase the risk of stomach bleeding, stroke and heart attack.