If you are interested in Japanese history, and in particular Japanese traditional dress, Jidai Matsuri should be on your must-see list.
The parade showcases all manner of dress, from the Meiji restoration all the way back to the Heian Period, and includes styles from all classes of life - from warriors and aristocrats, to historical figures and commoners. Viewing from the Imperial Palace or Heian Shrine locations is particularly memorable, as the dress in combination with the traditional surroundings feels as though you've been sent back in time. Along with the dress, the parade features traditional means of transportation, such as horses and cattle-drawn carts. It also has amazing omikoshi - large portable shrines that help spirits travel throughout the city.
All in all it was a wonderful experience to witness, and is unique in the fact that its the only Japanese festival I can think of to feature such decorative and interesting clothing from so many historical eras. Just be sure to arrive early, as the viewing areas get packed, especially near the Heian Shrine and Imperial Palace. Its less crowded along the city streets.