Ascender’s study found that the 10 most popular typeface families are: Poynter, Franklin Gothic, Helvetica, Utopia, Times, Nimrod, Century Old Style, Interstate, Bureau Grotesque and Miller. Further, 35 of the top 100 daily newspapers use a custom typeface or modified font in addition to retail, off-the-shelf fonts.

That was for American newspapers, by the way. My guesses at 10 more (European and American):

Frutiger
Minion
ITC Century
Corona
Univers
Escrow
Gotham
Whitney
FF Meta
FF DIN

… use a custom typeface or modified font in addition to retail, off-the-shelf fonts.

Some examples:
The Guardian family by Christian Schwartz
Floris and Taz by Luc(as) de Groot
Le Monde by Porchez Typofonderie

Also, have a look at the typefaces of Gerard Unger: several of them have been made specifically for the use in newspapers, like Swift, Coranto or Gulliver.

Swift should have been on my second list.

The Dutch newspaper nrc·next uses the entire Lexicon family — I quite like it.

Thanks!