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I get asked this once in a while and thought I would share. I'd like to know what the other experts here use, too.
One of my favorite resources is "American Metal Typefaces of the Twentieth Century" by Mac McGrew. It's very comprehensive and easy to use. Another one is the "Encyclopaedia of Type Faces" by Jaspert, Berry and Johnson. It's not as comprehensive or information packed, but it does give release dates and (more importantly) includes most European foundries. These are the two best resources I know of for identifying and getting information about metal typefaces.
For typefaces before the nineteenth century, John Berkely Updikes "Printing Types: Their History and Use" is useful. There seems to be a lack of good reference materials for type in the nineteenth century, except perhaps in printing museums and such. Rob Roy Kelly's "American Wood Type: 1828-1900" is good, but only covers (obviously) wood types.
For more recent typefaces (post-metal), FontShop's "FontBook" is good. It lists all the fonts they carry (thousands and thousands) and includes release dates (original and digital, in the case of revivals). Unfortunately, this is out of print right now. They are working on a new edition which should be out in the near future.
Another one I like is "The Solotype Catalog" by Dan X. Solo. This is especially good for identifying phototypesetting and film fonts from the sixties through the eighties.
Finally, there are some online resources that may be of some help, especially for more recent fonts:
I particularly like using the preview string features of MyFonts and FontShop. FontShop's facility has the added advantage of allowing you to copy the URL and paste it here to share the preview with others. (MyFonts used to have this, but they seem to have dropped it when they introduced the "live preview" feature.) It's very useful to enter your preview text before you start searching so that you can see it set in all the fonts that come up when you do keyword searches and such.
And I mustn't forget Mike Yanega's amazing Script Font Identification Guide:
Anyway, those are a few of my most-used resources. Perhaps once everyone has spilled their beans a summary could be placed in the TypoWiki.