By 
Republic of Korean Air Force Maj. Soon-Tae Park, 38th Fighter Group shows off Chegi skills a traditional Korean game at the New Years Day Joint Ceremony February 14. The New Years Day Joint Ceremony brought together Korean and United States Airmen to celebrate the Korean New Year. The Ceremony consisted of ancestor memorial services, New Year’s bow and traditional Korean food and games. U.S. Air Force photo/Senior Airman Jonathan Steffen
3:09 pm on February 20th, 2010 1
Traditional Korean game? Not really. It's popular all over Asia. Go to any park in China and you'll see people playing the game. It's very popular there. It's also the national sport of Vietnam (they are by far the best at it, I've read).
The correct English terms for the sport are "jianzi" (from the Chinese name of the game), "shuttlecock", and "feather football" (I think it's from a German term for the game).
The inventor of the hacky sack was inspired by the game, in case you wondered.