The Queen and Prince Philip do. When the Queen is "in", her Royal Standard flag flies from the roof of the Palace so we all know! And other members of the family have apartments there for when they are in London.
But at weekends, they go to Windsor Castle and in fact most of the family prefer it. Prince Andrew said once that they think of Windsor Castle as being more "home". Buckingham Palace actually hasn't been a palace for very long. Queen Victoria was the first monarch to properly move in, and after Prince Albert died she hardly ever went there, preferring Windsor or her seaside home at Osborne House on the Isle of Wight (which isn't a royal home any more and is open to the public - I have relatives a short walk away and I've been there). Buckingham Palace has certain problems as a home - one problem Prince Philip had to do something about was why the kitchens are so far from the family's dining room, so food always arrived cold - but it's convenient to be close to Parliament for the Queen's weekly meeting with the Prime Minister.
They also always go to Sandringham House in Norfolk for Christmas and it's a standard photo-opportunity for the press to take pictures of them going to the little church at Sandringham on Christmas morning.
Prince Charles and the Duchess of Cornwall live in Clarence House, just along the road from Buckingham Palace, where the Queen Mother used to live, and at Highgrove House in Gloucestershire: Prince Andrew lives in Royal Lodge at Windsor: and Prince Edward and Sophie and their children live in a large house in Surrey. Some "minor royals" have apartments in Kensington Palace.
8
Answers