One of the most « underground » place in Berlin, Teufelsberg is a former NSA listening station.

From Wikipedia :
Teufelsberg’s origin does not in itself make Teufelsberg unique, as there are many similar man-made rubble mounds in Germany (see Schuttberg) and other war-torn cities of Europe. The curiousness begins with what is buried underneath the hill: a Nazi military-technical college designed by Albert Speer. The Allies tried using explosives to demolish the school, but it was so sturdy that covering it with debris turned out to be easier.

The US National Security Agency (NSA) built one of its largest listening stations on top of the hill.

Let’s go straight to the point :

1. How to access Teufelberg’s NSA base ?
With the train (S-Bahn) go to the station « Heerstrasse », or drive to the street « Teufelsseestrasse » by car. Once there, walk/drive along one of the accesses shown on the map :

Teufelsberg Access from Berlin
The parking lot 2 is closer to the base by foot, but it’s definitely too far if you came with the train (then take the yellow path). If you take the green path, with the car or with bicycle, you might see savage pigs :)
Teufelsberg Access zoom
There is a hole located on the south part of the fence. It’s your best chance to enter. The main gate is quite dangerous to climb. If this hole does not exist anymore, take a walk along the fence, there are always new ones :)

Ugly teufelsberg's Guardian
There has been some people working on the most South-West building, and sometimes you might see this guy : —>

Don’t worry about them, these guys are just assholes and can not do anything against you. The workers will let you go without taking real care, but the bum-guard will take a picture of you, will not leave you alone until he sees you leaving the area and will claim that he is going to call the police.

To avoid those parasites, instead of taking the red path on the above map, take the blue one and go straight to the main building. Try to be as quiet as possible until you reached the main building. You should also be in peace if you go there late in the afternoon or on Sunday : avoid Saturday afternoon, cause in addition, it will be crowded.

2. Main spots
Teuflsberg main building
To me the most important thing to see is the main building, with the 3 listening balls on it’s top. To get in, first go on the West side of the building and climb the stairs till the 2nd floor (the 3rd one has been recently sealed), open the door and go to the center of the building. You’ll find there dark stairs, go up 2 levels, you will be on the roof of the building. Enjoy the view :
Teufelsberg roof
Teufelsberg Roof 2

It’s now time to get up there in the big listening ball. Just go back to the stairs and be courageous ! You can stop by on the levels to have a nice view on Berlin. Be careful though, this place is quite dangerous. You also might need to have some flashlight because the stairs are really dark at this moment. After the last level, go on with the stairs, you will reach a door. Enter, you will now be in the ball. Make some noise ! And again, enjoy the (small) view :
Inside Teufelsberg's listening ball
Go back to third floor of the main building, go on the left, you’ll see some former living quarter and also a cartoon-like door :
Cartoon door

You can now go back on the « ground », and if you think the boring guard/workers are not there head to the reception desk (top South building). You’ll find there the prison and the headquarters :
Prison + Assist Proctect Defend

3. Explore
Paintings, offices, roofs, basements, … if you feel like adventurous (and most important if you have light), just go around, you will always find cool stuffs to do/see
Teufelsberg - others