Any guidebook to Berlin is going to mention the flea markets that happen all around the city, mainly on the weekends and also sometimes during the week (here is a link to a list of each and every market, where they are run and their exact hours of operation. God bless German efficiency!) What are maybe less known to people from outside the city are the Troedellaeden (junk shops) that are scattered throughout each neighborhood. Though you can get vintage housewares, home decor and occasionally also jewelry, I personally think what they are best for is furniture.
My favorite Troedellaeden are the six or so lining Flughafenstrasse in Neukölln (U-7 Rathhaus Neukölln, between Karl Marx Strasse and Hermannstrasse). Basically each of these shops is a two to four bedroom ground floor apartment that is literally stacked floor to ceiling with tables, chairs, sofas, desks, you name it. Of course, a lot of it is pretty banged up, but their is still plenty of goodies to be found for an ever patient thrifting huntress. Most of the shop owners are likely to be male (German, Turkish or Arab), in their early 60s, reek of cigar smoke and probably speak little to no English but then it wouldn't be a true junk shop if anyone else were to run it.
Flughafenstrasse is far off the Kreuzkölln path (the area of Neukölln that has since become hip, though when I lived there five years ago it was basically a rat hole...) and is definitely not gentrified so you are also more likely to make a bargain. One of the shops, Trödel Klaus, even has a website which you can visit by clicking here.
Viel Spass beim Trödeln!