When you think of a royal palace, you usually think of one set building. In Copenhagen's case there are actually four distinct buildings which surround a large central square.
Why four? Apparently, because it was originally inhabited by four noble families. Only, when Christiansborg Palace burnt down in 1794 the royal family needed a new place to live. For the king and queen, it wouldn't do to live in the same palace lesser nobility had previous inhabited. The solution? Acquire all four noble houses and turn them into a super-palace.
While the Queen still uses some of the buildings as her winter residence, others are open to the public or converted into a museum.
This is also a fantastic spot to see the changing of the guard, and for a slice of history head to the corner facing the fountain (and opera house). Looking back into the square, you'll see a small patch of damaged stucco. That patch is an un-repaired piece of the palace that illustrates blast damage from WWII.