When is a 方言 a language and not a dialect I have always thought, perhaps wrongly, that it was mutual intelligibility that was the deciding factor as to whether a 方言 would be considered a dialect or it's own separate language.

Wikipedia's entry Dialect: Political Factors says:


  An opposite example is the case of Chinese, whose variations such as Mandarin and Cantonese are often called dialects and not languages, despite their mutual unintelligibility.


I'm not interested in politics, though; linguistically speaking when can a 方言 be considered a language and not a dialect?
I'm going to assume that the question you want to ask are how mutually intelligible various 方言 actually are. This 2009 study by Chaoju Tang and Vincent J. Van Heuven has some data on it.

Here's the excerpted table on how mutually intelligible various 方言 are:

Word Classification:
 

and 

Word Understanding:


You can read more on the methodology in the paper itself.

For comparison's sake this 1989 John B. Jensen study found that Spanish and Portuguese are 


  50-60% mutually intelligible at least as measured on...passive
  listening to electronically re-produced voices