You can buy excellent bread all over Berlin. A string of organic specialty bakeries have recently sprung up across town. They all bake bread in the traditional, time-consuming manner. Take the "Hofpfisterei" a small bakery chain from Munich, 100% organic and producing some of the best dark farmer rye bread (dunkles Bauernbrot) without any preservatives. Just rye and wheat flour added to water and salt! It's an admirable dedication to simplicity mirrored also in the German tradition of beer brewing.
An increasingly popular trend is for young people, especially in the Prenzlauerberg neighborhood of Berlin, to bake their own organic bread. Couples will meet up on weekends with their trolleys, babies, and organic veggies to see and be seen around the Kollwitzplatz, a hipster-filled park area with an über abundance of politically correct fair trade organic food shops nearby selling delicious fresh-baked bread. (You'll meet very few Berliners here, mostly just tourists complaining about other tourists.)
For the best bread, I recommend the many Berliner weekend markets. Must-try German breads include the famous salty Laugen Brezel (pretzel) which you'll want to accompany your beer, aka liquid bread. The dark brown gorgeous looking sourdough-based Pumpernickel from Westphalia is another distinct German bread often used for hors d'oeuvres.
The most popular German bread must be the plain-looking and tasting Brötchen (white breadroll), eaten for breakfast with jam and for lunch with butter and slices of cheese or salami, or simply served beside your wurst (sausage). I always use three-day-old pretzel bread in my meatballs and for my knödle (German potato and bread dumpling).