Denmark's National Museum has an incredible collection of Viking weaponry, gold, and rune stones, as well as Egyptian mummies, Assyrian reliefs, Persian ceramics, Etruscan gold jewelry, and Roman household utensils. Among the many highlights is a finely crafted 3500-year-old Sun Chariot, as well as bronze lurs (horns), some of which date back 3000 years and are still capable of blowing a tune. There's an excellent children's wing to the museum, where kids can play at being teachers, Vikings, knights, and shopkeepers.
You'll find sections related to the Norse and Inuit people of Greenland, and an evocative exhibition called Stories of Denmark, covering Danish history from 1660 to 2000. Among the highlights here are recreated living quarters (among them an 18th-century Copenhagen apartment) and a whimsical collection of toys, including a veritable village of doll houses. The museum also has an excellent Children's Museum, as well as a classical antiquities section complete with Egyptian mummies.
For a little cerebral relief, find refuge in the well-stocked gift shop.