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As Kahis says there is no universal agreement . Ranking is the problem. The family (for Linnaeus the Genus), though, is the most readily recognized taxon (see Glossary for this term) in Diptera.

Also see Glossary info for the family (See top left menu Then>F > then family "The two suborders of Diptera are divided thus: the Nematocera are divided into 77 families of which 35 are extinct ( fossil only ) and the Brachycera are divided into 141 families of which 8 are extinct."

For a list see
Links: http://en.wikipedia.org/wiki/Families_of_Diptera At the bottom is an old but still very useful download Family Group Names in Diptera and Bibliography by Sabrosky
There is also the Classification link (top left again) and it's explanatory note, but not for World species.

Cheers Robert