Question pretty self-explanatory. Should the abbreviation of the Latin term philosophiae doctor be written as PhD (no periods) or Ph.D. (with periods)?
Actually both are correct, I could easily found both on my NOAD, and there's plenty of pages on the net where you find it written as "PhD".
The OALD gives an interesting distinction, stating that Ph.D. is especially North American English.
Now, being a non-native speaker, I can only rely on official sources to state who uses what, but there's no doubt that both variants are used.
Lastly, I think there's really no point in distinguishing them as "Philosophiae Doctor" or "Doctor of Philosophy" because it's the same exact expression, although considering the abbreviation, the former is the correct and original long version, the latter is just the English translation.
I remember discussing this with a trained secretary a long time ago. We eventually decided that the use of camel case (starting each abbreviated word in upper case) removes the need for the periods when abbreviating titles. However, when an abbreviation is relatively new or used in an unusual context, the periods help to avoid ambiguity.
For my own use, the overriding consideration is 'house style'. It is more important for a document to be internally consistent, to avoid confusion.