Heir-to-the-throne prince Charles is a keen polo player, while prince William is president of the Football Association, the game's governing body in England.
Queen Elizabeth praised the power of sport in bringing people together in her Christmas Day address to the nation, before London hosts the 2012 Olympic Games.
The queen said events in 2010, including the soccer World Cup in South Africa and the Commonwealth Games in India, showed how important sport is in uniting people from different backgrounds and of different ages.
"These kinds of activity are common throughout the world and play a part in providing a different perspective on life," she said, in a message recorded at Hampton Court Palace in London.
"Apart from developing physical fitness, sport and games can also teach vital social skills.
"None can be enjoyed without abiding by the rules, and no team can hope to succeed without co-operation between the players. This sort of positive team spirit can benefit communities, companies and enterprises of all kinds."
The first Christmas broadcast was delivered by George V in 1932 and has become a traditional part of the Christmas Day festivities for many in Britain and around the world.
The 84-year-old monarch has made a Christmas broadcast in every year but one since her 1953 coronation. Unlike her speech at the annual opening of Parliament, she expresses her own views rather than those of the government.
Her theme this year reflects the royal family's keen interest in sport, particularly horse-riding.
The queen owns and breeds race horses. Her daughter Anne, the princess Royal, represented Britain with the three-day eventing team at the 1976 Montreal Olympics.
Anne's daughter Zara Phillips is also an event rider, winning individual and team gold medals at the 2005 European Eventing Championship. She was picked for the equestrian team at the Beijing Olympics in 2008, but missed them due to injury.
Heir-to-the-throne prince Charles is a keen polo player, while prince William is president of the Football Association, the game's governing body in England.
Members of the royal family are spending Christmas at the queen's country estate in Sandringham, eastern England. They greeted well-wishers who waited in the bitter cold after a Christmas Day church service.
Prince William, who announced his engagement to Kate Middleton last month, was not there as he is working with a Royal Air Force search and rescue team in North Wales.
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