Prado: One of the great art museums in all the world, this gem has an enormous collection of 12th to early 19th century European art. It is famous for its variety of pieces by Velasquez, Goya, and El Greco. I like the easiness and space afforded by the building to make it a relaxing place to visit. Americans may not be as familiar with these Spanish classics compared to those of a museum like the Orsay or Orangerie in Paris. I would suggest getting a personal guide or audio guide for the tour.
Thyssen-Bornemisza: Located across the way from each other, the Prado, the Thyssen form the "Paseo del Arte" in Madrid. For me, it is the perfect compliment to the Prado. Since the collection was originally derived from a private collection, expect a wide variety of art. Vistors will find Van Gogh, Monet, Rubens, Rembrandt, Carvaggio, The Thyssen contains significant works from the Impressionists and Post-Impressionists. Travelers enjoy the work of Van Gogh, Monet, Degas, Renoir. More classic pieces from Renaissance painters like Rubens, Hopper, Degas, Picasso and Mondrian. It's a fun place to visit.
Reina Sofia: It's worth the visit for just one piece: Guernica by Picasso. This anti-war statement is the most powerful painting I have ever seen. But let's not sell the rest of the museum short. It's excellent collection of 20th century art, primarily by Spanish artists but other familiar names like Ernst, Man Ray stand next to those like Picasso, Miro and Dali.