Step one is to create a new admin user account, log into it, and see if the problem persists. If that doesn't do the trick, see Font Management in OS X. There might be an answer in there.
Then, OPTION-click on the Finder's GO menu, select Library, drill down to the Preferences folder and make a list of the plist files shown there. Log out and back into the original user account and put the plists from your list into a new Desktop folder, restart, and boot into Safe Mode (hold down the SHIFT key when restarting). That should clear the font cache. Then restart normally and log into the original account. Font book should work. If so, move some of the previously moved plist files back and log out and back in. This latter step is only necessary if you don't want to reset the prefs for the moved items. Repeat until you identify the conflicting or corrupt files.