Well, for instance, here’s the page on the Chinese branch of the Sino-Tibetan language family from Ethnologue:
http://www.ethnologue.com/show_family.asp?subid=1270
They consider that there are 14 languages which are part of the family, including Dungan, which is not usually called Chinese because it’s spoken in Kyrgyzstan, although it’s just as closely related.
In The Cambridge Encylopedia of Language by David Crystal, it says that although they are frequently referred to as dialects, it would be more accurate to think of them as 8 different languages, since they are not mutually intelligible.
In The World’s Major Languages edited by Bernard Comrie, it says that it would be linguistically more useful to refer to them as separate languages, although for political purposes they are frequently referred to as dialects.
In The Atlas of Languages: The Origin and Development of Languages throughout the World edited by Bernard Comrie, Stephen Matthews, and Maria Polinsky, it says although they are frequently referred to as dialects, Cantonese differs from Mandarin as much as Italian differs from French.
Here’s a website that speaks of them as 7 different languages:
http://www.chinalanguage.com/Language/chinese.html
Here’s an Encyclopedia Britannica article that says that, although they are frequently referred to as dialects, they are really different languages.
http://www.britannica.com/eb/article?eu=118135
I think a summary of the sources I’ve just checked would be that linguistically it would be better to think of them as different languages (some of which have highly divergent dialects within them), politically many people would prefer to call them dialects.
In fact, I think that politics is what’s preventing an accurate assessment of the linguistic situation in China. The Chinese government is desperately trying to hold the country together despite the wide variations in language and many other things. For instance, there’s only one time zone in China (although it would more properly be split up into five of them) because they want to avoid any thought of regionalism in the country.
And what are your sources?