Video games have been around for at least 50 years now. Odds are, video games as a concept are older than you are.
And, if you want to study the history of games dating back to the age when transistors were revolutionary, you should go to the Computerspiele Museum of Berlin: the Berlin Video Game Museum.
Connected TravelerI toured the Computerspiele Museum during my trip to Berlin for IFA 2015, and I saw some genuine artifacts of video game history.
The museum is located on Karl-Marx-Allee 93a, just outside the Weberweise U-Bahn (subway) station on the U5 line. It's open daily from 10 a.m. to 8 p.m. Besides the big sign over the door that says Computerspiele Museum, you can tell what it is as soon as you enter, because of the life-sized Link statue facing down the life-sized Jak statue right next to the admission desk. It's 8 euros to enter, or 6 euros if you get a Berlin tourist pass (recommended if you plan on sightseeing, since it includes a U-Bahn pass and discounts to other musems).
The museum spreads over one floor, and tries to stack the entire history of gaming into a few corridors and still leave room to play. Past Link and Jak (and statues of Gordon Freeman and both the PlayStation-era and modern Lara Crofts) are walls covered in video game equipment dating back to vintage Computer Space and Pong cabinets.
The exhibits also include a giant, functional Atari 2600 joystick playing that horrible 2600 port of Pac-Man, a wall of game consoles showing every major step from the Magnavox Odyssey to the current generation, and a series of mock-up rooms depicting classic game setups of the 70s, 80s, and 90s. There are also 22 video stations controlled by joysticks; you can rotate a cube that will play one of several videos, like game commercials and developer interviews, that relate to nearby exhibits.
In side rooms, you'll find playable 80s arcade classics including Frogger, Pac-Man, and Centipede (the trackball is a little sticky), and a set of playable summer-themed games on various classic consoles: NeoGeo, GameCube, Sega Master System, Dreamcast, and more. Far in the back, you can play an authentic 80s East German arcade machine full of Communist-themed games. They're pretty bad, but they're definitely part of history.
If you can't make it to Germany, video game exhibits are spreading across the U.S. The Strong Museum in Rochester, NY has a massive collection and a semi-permanent exhibit called "eGameRevolution" where you can play them. A touring Smithsonian exhibit on the history of video games has been on the road since 2012; it's currently in Memphis, and will hit Miami from October through January 2016. And a permanent National Videogame Museum is being constructed north of Dallas in Frisco, TX.