Cycles: What does the nodes do and most basic usage?

I am trying for some time now to understand the different nodes that cycle offers.
Yes I do know it is not finished, still there is a lot of interest and I just can’t help but play around with it.
The lack of documentation only leaves me the poking around approach, which in many cases does always give me any result.

Mostly I am missing some very basic usages for the different outputs.
A very simple one is attached for the backfacing output of the geometry node.
A UV-Sphere cut in half so you could see the outside and inside of it.

I wish there were something like this for the other nodes as well.
Especially for the Light Path nodes. (I know about the Wiki page: but it does not explain what I can actually do with the output. In which node should I plug this output to get any visible result?)

If there is enough demand and if it is allowed, I would volunteer to add specific pages to the wiki. In my opinion it should be documented there.

So what is the most basic setup to see some of the node outputs in action?