Apparently you can!
Old dogs may not learn as quickly as they did when they were young, but with time and patience, most older dogs can be taught to do anything that a young dog can.
Here's proof that they can, check out this video from one of my favorite shows Mythbusters:
With the help of professional dog trainers, Adam and Jamie were both able to teach two old dogs (Bobo & Cece, a pair of 7-year-old brother & sister Alaskan Malamute) sitting, heeling, staying, shaking hands, and lying down. However, Cece was the more obedient of the two dogs as Bobo had trouble staying.