I added two planes in Cycles with Image Texture in png with some transparency. I covered one by the other but transparency doesn't work, I mean it is impossible to see the one which is under despite transparency in the one which is above. What could be the problem?
As @gandalf3 pointed out, you can check out the answer here. I'll redo it with a bit more detail though.
I'll assume you've already UV mapped your plane (select plane, go into Edit Mode, U > Unwrap) and you already set up the texture in the Materials tab to look like this:
So, you render and the alpha appears as black.
To fix this, you go into the Node Editor and you use the alpha information to set where the plane should display the texture image and where it should have transparent material.
Render and you should have transparency.