Trying to understand the charecteristics of a font face, i've been going through a lot of books and sites. Though there are innumerable classifications, there are 9 broad categories which give a better understanding of the subject. I am not going to dwell in detail about them here, rather will give few useful links.
1. Humanist
2. Garalde
3. Transitional
4. Didone
5. Slab-serif
6. Lineale
7. Glyphic
8. Script
9. Graphic / Decorative
http://jeff.cs.mcgill.ca/~luc/britishstandards.html http://www.typography-1st.com/typo/classtyp.shtml
http://www.redsun.com/type/classification/