How is it possible to determine the fonts used by text in PDF and TIFF files?
For TIFFs or any other raster (pixel) image, Jin’s answer covers it.
For PDFs (assuming it’s a ‘proper’ PDF and not a raster image embedded in a PDF, as produced by scanning/fax software), font information is embedded in the file.
In Adobe Reader, Adobe Acrobat, and Foxit Reader 3 — probably slightly different in other applications — File menu > Properties > Fonts tab gives you a list of all fonts used in the document.
There are also third-party plugins for Acrobat, such as Enfocus PitStop Pro, which add the ability to find/replace/report on instances of a particular font throughout a document.