Pena Palace, Portugal

Yellow domes, a red clock tower and gray battlements piled on a hilltop above Sintra, near Lisbon. Pena is the most colorful palace in this gallery, and the mix of styles is deliberate. King Ferdinand II, the German-born consort of Portugal's queen, bought the ruins of a hilltop monastery that the 1755 earthquake had wrecked, and from 1842 to 1854 turned them into a summer palace, with Baron Wilhelm Ludwig von Eschwege leading the design. Gothic, Manueline and Moorish touches sit side by side, which is why it feels invented rather than inherited. It belongs to the Cultural Landscape of Sintra, a UNESCO World Heritage Site since 1995, and the forested park around it hides more follies to find on foot.