Is there any way to force Microsoft Outlook to always reply in HTML format?

There is no option in Outlook to change this default; Outlook will always reply and forward in the same format (Plain Text, Rich Text or HTML) of the original message. This is to keep the original message intact, maintain the preference or technical limitation of the original sender.
For instance, several mail clients on mobile devices do not support HTML formatted messages and HTML formatted messages are also larger than the Plain Text equivalent.

If you still need to change the message format, you can do this manually or automatically via an add-in.

Manually changing the message format

If you want to change the message format when replying, you can do so in the following way;

  • Outlook 2003 with Outlook as the e-mail editor
    Format-> HTML
    If the current message is in Rich Text format, you’ll first have to convert it to Plain Text.
  • Outlook 2003 with Word as the e-mail editor
    On the e-mail Toolbar which also hold the Send button there is a dropdown list right next to the Options… button to change the message format.
  • Outlook 2007
    tab Options-> button HTML
  • Outlook 2010 and Outlook 2013
    tab Format Text-> HTML

Re-insert your signature

After you change the message format to HTML, your signature template won’t be restored to its original HTML version.

To restore the signature to its HTML design, you’ll need to select it again from your list of signatures in Insert-> Signature.

Another way to do this is by right clicking somewhere within your signature text and select your signature again (for Outlook 2003, this requires you to have Word set as the e-mail editor.