Museum für Kunst und Gewerbe Hamburg is one of the most interesting museums I have visited. The permanent collection provides a curious mix of ancient art, design, photography and new media, graphic art, art nouveau, ceramics, fashion, multicultural arts, instruments, and period rooms. Each of the collection rooms were compact so that you didn't feel overwhelmed by the exhibits while remaining comprehensive and all encompassing of the history. The museum was also hosting a very interesting tattoo exhibition as part of their temporary collections.
I specifically enjoyed the ancient art collection made up of 5500 artefacts from the ancient Near East, Egypt including Greek, Etruscan and Roman art. The Egyptian stone vessels, amulets, and statuettes received most of my attention as the museum housed plenty of artifacts I had never seen before.