Berlin's Kunstgewerbemuseum is Germany's oldest museum of decorative arts, with European furniture, textiles, glass, porcelain, metalwork, fashion, and design objects from the Middle Ages onward. The Kulturforum branch is the main stop for most visitors.
It is especially good if you like the material side of history: chairs, cabinets, church treasures, courtly objects, and modern design rather than paintings alone. The museum also has a second section at Kopenick Palace, so check which collection you want before setting out.