For Googlers, since I had terrible trouble finding this. Information originally from here.
How to set Outlook to always reply in plain text, regardless of the original email format:
In Outlook, click Tools -> Options
In the Preferences panel, click “E-mail Options”
Tick the boxes for “Read all standard mail in plain text” and “Read all digitally signed mail in plain text”
The above instructions work for Outlook 2003 – the link has instructions for other versions. It requires that emails are always read in plain text, but it’s the only method I can find that doesn’t macros, weird HTML stripping programs or reconfiguration for every email.
I looked at that options panel at last twice while trying to figure it out, not sure how I missed it!