If you are somewhat familiar with the German academic system, you might be aware that different disciplines award different types of doctorates. While the list at the German language Wikipedia is quite long, you normally encounter only a few (as listed in the English language Wikipedia).
Three very common doctorates are the Dr. rer. nat. ("rerum naturalium") in sciences, the Dr. phil. ("philosophiae") in humanities, and the Dr.-Ing. in engineering. For Computer Science, which type of doctorate you are awarded depends on your university: Most departments award exclusively a Dr. rer. nat., some exclusively a Dr.-Ing., some allow the candidate (or the advisor) to choose between the two, and a few do something totally different (again, see Wikipedia).
When my alma mater, Goethe University in Frankfurt am Main, was founded back in 1914, the physicists did not want the Dr. rer. nat. for their department. Translated literally, "rerum naturalium" means "natural things", and one of the founders claimed that you can only be a doctor of a science, not a thing (where I use "science" as translation of the German "Wissenschaft", which does not distinguish between humanities and natural sciences).
Thus, Goethe University decided to be the only university that uses Dr. phil. nat. instead of Dr. rer. nat. as abbreviation of "Doktor der Naturwissenschaften". (This story was apparently forgotten and only discovered a few years ago by the university archivist, at least according to the university newsletter.) Decades later, Computer Science was introduced, and as Goethe University has no engineers, the natural sciences doctorate was the natural choice.
To cut a long story short: "Dr. phil. nat." means "Actually a Dr. rer. nat., but from Goethe University, because we are really special, unique snowflakes".
This whole stuff is needlessly complicated, as you do not address people with all this abbreviation stuff between the "Dr." and the name. Even if you are very formal, you'd only say or write something like "Sehr geehrte Frau Doktor Name", or in my case, "Sehr geehrter Herr Doktor Freydenberger". In particular, you never, ever include the lower degrees (in my case, Dipl.-Inf. for "Diplom-Informatiker") - unless you are dealing with engineers.
Personally, I prefer if people do not address me with my doctorate (unless that means I get some preferential treatment, which is very rare). But that whole phil. nat. business needed to be explained.
Update from July 2015: I just discovered that Goethe University changed this in December 2014. Some of the departments, among them Computer Science, switched to rer. nat., which means that, after a transition phase, there will be no more Dr. phil. nat. in Computer Science.