The Computerspielemuseum in Berlin claims to have been "the world's first permanent exhibition devoted to digital interactive entertainment culture."
travel.stackexchange.com/users/1371/Michael Borgwardt
Jan Orna has put together a comprehensive list of European arcade museums (all with over 20 playable machines):
Freddy's Pinball Paradise , Echzell, Germany Deutsche Flippermuseum Extraball , Neuwied, Germany Arcade Hry , Cerveny Ujezd, Czech Republic Pbal Gallery , Budapest, Hungary
For Amusement Only , Seligenstadt, Germany Muzeum Arcade , Moravska Trebova, Czech Republic Baboon City , Herning, Denmark RetroGames , Karlsruhe, Germany Spilmuseet , Ikast, Denamrk Big Ben Matic , Lignano Sabbiadoro, Italy Museum of Soviet Arcade Machines , Moscow, Russia Arcade Street , Paris,
France Museum of Soviet Arcade Machines , Saint Petersburg, Russia Sportland, Blankenberge, Belgium Oldenburger Computermuseum , Oldenburg, Germany Hearth of Gaming , London, U.K. Geek Room , Asnieres sur Seine, France Timewarp
Arcade , Bridgewater, U.K. Lunapark Reflex , Oostende, Belgium Be sure to check out the full site , as it has stats on each of the arcades, pictures, and more details.
Depending on your definition, arcade museums may or may not fall under the category “video game museum”.
I'm leaving this as community wiki
so there can be 1 canonical arcade museum answer
travel.stackexchange.com/users/15304/Michael Kropat
If you are going to Italy, the Video Game Museum
ViGaMus in Rome will be the place to visit.
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Arcade Planet in Seville, southern Spain, is open every weekend afternoon, and has more than 100 arcade games.
The industry of video games designed for arcades, ceased to be present in Europe at the end of the year 2000.
The new generation of domestic video games, abusive taxes, and the crisis caused that the recreational machines stopped being manufactured, and the most serious ... that these systems were destroyed so as not to pay the monthly fees that their owners had to pay just for having them.
In Arcade Planet, we have managed to rescue and restore the best recreational games in history, while preserving the best games of all systems.
Arcade Planet offers its incredible collection of Arcades for events, exhibitions, organizanazación of tournaments, and sessions of free game "free play".
With this initiative, those who played in the 80's and 90's will remember the best moments of leisure in their lives ... and the new generations will discover the special interpretation of the game mode created for recreational salons ... where the only purpose is immediate fun.
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The Centre for Computing History in Cambridge, UK has an extensive selection of old computers and gaming consoles, many powered on and set up ready to be played.
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I'm looking for a museum that collects video games. Preferably, the museum should be located in Europe.
Is there a video game museum anywhere in Europe?
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The  Computerspielemuseum  in Berlin claims to have been "the world's first permanent exhibition devoted to digital interactive entertainment culture." Arcade Planet in Seville has more than 100 arcade games, and the Centre for Computing History  in Cambridge, UK has an extensive selection of old computers and gaming consoles, many of which can be played. Video game museums can be found in Berlin, Seville and Cambridge.
Video game museums can be found in Berlin, Seville and Cambridge.