One of the problems with this is that now Windows 'hides' the file name extension by default. So its a good possibility that a user won't know that a Word file is a "doc" or "docx" or that "odt" is open document text.
If you want an idea of how many different file extensions there are, take a look at
http://www.fileinfo.com/filetypes/common or
http://en.wikipedia.org/wiki/List_of_file_formats. Also, just to make life a bit more difficult, take a notice of how many different files use the same extension (DBF — db/dbase II,III,IV and V, Clipper, Harbour/xHarbour, Fox/FoxPro, Oracle; FDB — Firebird Databases and Navision database files; etc).