For visits to Berlin, pack as you would for an American city: dressy outfits for formal restaurants and nightclubs, casual clothes elsewhere. Jeans are as popular in Germany as anywhere else, and are perfectly acceptable for sightseeing and informal dining. In the evening, men will probably feel more comfortable wearing a jacket in more expensive restaurants, although it's almost never required. Many German women wear stylish outfits to restaurants and the theater. Note that Berlin is windy, which can be quite pleasant in summer but a complete bear in winter, so pack warm clothes in for the latter.
To discourage purse snatchers and pickpockets, carry a handbag with long straps that you can sling across your body bandolier style and with a zippered compartment for money and other valuables.
For stays in budget hotels, pack your own soap. Many provide no shampoo or soap at all or only a small bar.