I need a cylinder or sphere, which has all normals directed inwards. Sounds strange, but I want to place my VR-Camera inside of this cylinder and use it kinda like a skybox. I know, that I can let Blender set all my normals to the outside, but is this possible for the inverse, too?
To flip the normals of your cylinder, Tab into Edit Mode and key T to toggle open/close the Toolshelf. Go to the Toolshelf > Shading/UVs tab > Shading dropdown > Normals section and click Recalculate. This will align all the normals. Now, you can click Flip Direction to align the normals on the inside of the cylinder.
Note that as lemon said in the comments, Ctrl + N is the shortcut for Recalculate, and Shift + Ctrl + N is the shortcut for aligning the normals to the inside of (an object), not flipping them, aligning them to the inside of an object.
To check your work, first, make sure the exterior and interior shading has been flipped. Next, key N to toggle open/close the 3D Viewport Properties panel and go to the Mesh Display tab. I like to turn on Face Normals. Now, every normal will appear as a little blue line in the center of each face.