I had tried deleting font directories (as suggested) and also had replaced all my fonts from a friend's computer - to no avail. On a tip, I created a new user, logged in and found that Word worked perfectly. This meant that the problem was somewhere in Word's user settings for my primary user.
I dug down and found Word keeps two files in
/Users/Library/Preferences/Microsoft/called Word Font Substitutes and Word Settings (10). I deleted both of these and Word started perfectly, re-generating the files. After closer analysis I discovered that it was Word Settings (10) which had caused the problem.

