Welcome to the club, I have the same problem, using Cinema 4D R11.0 and Unity 2.6 (same on 2.5). The really nice help I got so far from here: Make sure you have it UV mapped! I did so, but same problem, no textures. It looks like its not so easy peasy as its described… I hoped it would be fixed in 2.6, but unfortunately not.
I also tried to export/imprt as FBX and 3DS, but all the same. Once it just got black but that was it. All this on a very simple object…
What fixed it for me was when I exported my cinema file as a 3ds file. for some reason unity couldn’t import my UV data directly from my c4d file. as soon as I converted it to 3ds it worked perfectly.