Tucked inside the Smithsonian American Art Museum, until Sept. 30, 2012, is the Art of Video Games Exhibit. For anyone with an appreciation of Video Games, this is a must visit exhibit, so try to get yourself to Washington, DC before it leaves!
In the exhibit, you'll find many different video game "artifacts" from the young history of video games, dating back to the late 1970's. My favorite (shown above) is the cloth map from Ultima IV... I still remember having this as a child!
You'll also have the opportunity to play some classic games such as Super Mario Bros. and The Secret of Monkey Island (shown above). After this section, you can see videos of all the major game systems and some of the most historically impacting games of those systems.
While the rest of the museum does have plenty of great art to see, this exhibit is the one you don't want to miss!