I'm not a big club-goer. I prefer to hang around in Pubs ("Kneipen") and bars. Some of my favourite bars are:
in Mitte:
Some years ago I used to hang around a lot in Oranienburger Straße, but since this became a real tourist attraction, I don't like to stay there any more. But if you'd like to go there, I would recommend you to have a look at the "Tacheles", or maybe visit the "Assel", a pub which is still kind of cosy.
In this area (around Helmholzplatz), you can find lots and lots of bars, cafés and restaurants, so discover for yourself, which ones you like best!
Furthermore I like in Prenzlauer Berg:
One place you should never go is the "An einem Sonntag im August" in Kastanienallee (although Kastanienallee itself is worth a visit). The food is lousy and the service is bad, because the owners are too greedy to employ more staff. Believe me, I worked there once! :-)
Visist the area around Wiener Straße/Oranienstraße/Manteuffelstraße! You will find lots and lots of pubs there!
for German speakers: http://www.boxhagener-platz.de
Have a look at the area around Nollendorfplatz and beyond (Maaßenstraße, Akazienstraße), especially on Saturday when there is a big market!
Note: Unlike in other cities e.g. London, in Berlin you have a lot of pubs and bars and the "alternative scene" in certain areas of the inner-city boroughs. This is also the cause (or maybe the effect?) why some of the inhabitants of each borough have a certain kind of "local patriotism". I know e.g. some people living in Kreuzberg, who won't set a foot in Charlottenburg or Schöneberg, much less in any suburbian borough.
Of course, these areas suffer a lot from gentrification, like the area around Kollwitzplatz in Prenzlauer Berg. In the beginning and the middle of the 90ies, you could find a large number of independent cafés, clubs and bars there, some of them were a relict from the former separation of Berlin, like the "Café Westphal" in Kollwitzstraße. Since the middle of the 90ies, more and more of these nice locations had to close down when property prices rose and restaurants opend which even fed guests like Bill Clinton.
Another note: Winter in Berlin is really terrible. But if you know some nice people and some comfortable and cosy places, you can have a really good time. And, another advantage: Even if you stay out boozing until 6 - 7 o'clock in the morning, it's still dark when you go home! ;-)
And: The more terrible the winters are, the more wonderful are the summers! If possible, visit Berlin in summertime! Have a look at all the huge parks around the town - the Tiergarten is the biggest one (where also the annual Love Parade takes place), but the nicest one is the Volkspark Friedrichshain (because that's close to where I live ;-) ), even in winter. If you visit it in summertime, you should definitely have a beer at one of the beer gardens around there - one is in the park (behind "Café Schönbrunn"), another one is just next to the Cinema "Filmtheater Am Friedrichshain". If you are in Prenzlauer Berg around the area of U-Bhf. Eberswalder Straße, you should have a look at the tiny Mauerpark ("wall park") in Eberswalder Straße for the spirit there is very nice. More nice parks:
If you're looking for a strange and martial experience, go to the Michael-Kirch-Platz in Mitte on a Sunday afternoon and watch the Jugger on their weekly training. Don't be afraid, they're just playing! ;-)