The Royal Palace (Kungliga Slottet) is one of Europe's largest palaces, with over 600 rooms spread across a massive baroque structure in Gamla Stan. It serves as the official residence of the Swedish monarch, though the royal family actually lives at Drottningholm.
Several museums operate inside, including the Treasury with the crown jewels, the Armoury, and the Museum of Antiquities. The daily changing of the guard ceremony in the outer courtyard draws crowds, especially in summer -- it takes place around midday and is free to watch. Allow a couple of hours if you want to see the state apartments and at least one museum.