Configure Thunderbird to never send (or even try to send) HTML emails
Solution 1:
One way to accomplish this is to turn off "Compose messages in HTML format", which is under your account settings, in "Composition and Addressing". This will also get rid of the HTML editor, which can be useful even for plain-text messages. (e.g., it nicely formats lists)
The other way which preserves the HTML editing features, but auto-converts to plain text, is Preferences -> Composition -> Send Options -> Text Format, select "Convert the message to plain text" instead of "Ask me what to do".
Solution 2:
Tools > Account Settings > Composition & Addressing > Untick "Compose messages in HTML format".
Solution 3:
The following Information is current for version 17 of Thunderbird, taken from the official FAQ, and answers the question. I post this to update the information provided by the answers from '09.
Specify that messages should be composed in HTML format (for the selected account)
Menu location: ToolsEdit | Account Settings | <account name> | Composition & Addressing
The answer given by derobert is wrong as of (at least) version 17, as there are only options regarding how to format HTML messages at that location.