Non-EU PhD title in Germany
How your PhD is counted depends a lot on from which country you obtained it. Currently, degrees from Australia, Canada, Japan, Israel, and most doctoral-granting American universities are recognized as fully equivalent to "Dr." Beyond that, however, the PhD is listed as a PhD, so long as it's been granted by an institution accredited to give out doctoral degrees. (It has to be legitimately "earned.") You just would not technically be allowed to call yourself "Herr Dr. Hans Wurst"; you'd be "Herr Hans Wurst, Ph.D." (or whatever the formal name of your degree is). 

Unfortunately, the classification of the degree does matter in Germany. Someone who holds a Dr. rer. nat. (sciences), for instance, will have a harder time getting a position in an engineering faculty than someone who holds a Dr.-Ing. (engineering). PhD's may or may not count as being equivalent to either degree, unless the specific regulations of the universities allow for this. (This can make a difference in setting up thesis committees, depending upon the regulations of the faculty in question. Yes, it's really annoying, but that's the way the system is set up.)

Fortunately, as Nate says in his answer, the rest of the world is nowhere near as strict as German law (even the modified version now in effect).

Also, you can apply to the Zentralstelle für ausländisches Bildungswesen (Central Authority for Foreign Education) for recognition of a foreign-obtained degree as equivalent to the corresponding German degree.