Science Museum (London)

Launchball: physics game

http://www.sciencemuseum.org.uk/launchpad/launchball/

Rizk: climate change defence game

http://www.sciencemuseum.org.uk/ClimateChanging/Rizk.aspx

Thingdom: genetics and evolution sim

http://www.sciencemuseum.org.uk/whoami/thingdom.aspx

Smithsonian and MIT

Vanished: transmedia treasure hunt for school kids, must use genuine scientific method to solve clues

https://vanished.mit.edu/

Wellcome Collection

Memory: a simple card memory game based on pelmanism using images from Wellcome Images
http://www.wellcomecollection.org/memory

High Society quiz: a multimedia multiple choice quiz built using a quiz engine
http://www.wellcomecollection.org/highquiz

Filth Fair: an iOS-based puzzle game to support an exhibition called Dirt.
http://www.wellcomecollection.org/filthfair

High Tea: a strategy game based on the 19th-century British opium trade in China, to support an exhibition entitled High Society about drugs
http://www.wellcomecollection.org/hightea

Axon: a fast clicking game about foetal neuron development in support of the Brains exhibition.

http://axon.wellcomeapps.com/ 

Tate

Tate Trumps: top trumps with artworks, free iOS game

http://www.tate.org.uk/modern/information/tatetrumps.shtm

Wondermind: Alice in Wonderland and neuroscience for a younger audience

http://wondermind.tate.org.uk/ 

J. Paul Getty Museum

GettyGames:  three casual games with JPGM collection (card memory game, image switched, find details), and puzzles

http://www.getty.edu/gettygames

Art Sets and Art Treasure Hunt on Whyville.net (log in required): Art version of card game Set, and a treasure hunt with JPGM collection

http://www.whyville.net/smmk/top/gates?source=getty

Detroit Historical Society (and Eduweb)

Building Detroit: One family, five generations, countless ways to build a city.

Minnesota Zoo and Eduweb

WolfQuest: Live the life of a wild wolf in Yellowstone National Park.

USS Constitution Museum  (and Eduweb)

A Sailor's Life for Me! Role-play game about the life of a sailor on Old Ironsides during the War of 1812.

Mount Vernon (and Eduweb)

George Washington's World for Kids - Several 3D games about the life of America's first president.

National Air & Space Museum, Smithsonian Institution (and Eduweb)

Design an Air Racer: Design an airplane to win exciting races in the Golden Age of Aviation.

Tuskegee Airmen Flight Leader: Step into the flight suit of a Tuskegee Airmen—America's first black fighter pilot squadron! (Scroll down the page to launch the game.)