I visited the Museum für Naturkunde a few days ago during a business trip to Berlin, and it is together with the Technikmuseum one of the must-see attractions in the city.
The mineral collection alone, organized largely systematically, covers thousands of specimens and can easily keep you busy a whole afternoon. I've included some pictures below. The crowd seems to be more interested in the giant dinosaur skeletons than in the mineral exhibits, so you have all the time in the world to enjoy the collection without being overrun by screaming kids, as is often the case in other museums.
For the fossil enthusiasts among us, the crown piece of the museum is its Archaeopteryx skeleton, the most complete of 13 specimens ever found (call it the Type Locality of the species!).
Best regards,
Yannick