How can I view the HTML of a Thunderbird e-mail?

If you're in mail composition mode, which it sounds like your are, forget the "view source" option people are telling you.

You want the HTML, not the raw email message with MIME formatting and everything.

Instead, while in composing the message, Edit->Select All, then click the Insert->HTML menu option on your message window.

The window that opens is small, but you can drag the window to a larger size.Your HTML message will be there (minus headers and body tags). This is more useful to copy a message out as HTML.

Likewise, you can create your message in your favorite HTML editor, and insert it using this feature as well.

Though the menu command is Insert->HTML, it really allows you to edit the message as HTML as well as long as you select the text before you invoke Insert->HTML.

I use this often when forwarding a message that was a poorly designed email newsletter and I need to tweak a few things before forwarding on.

You can send yourself a copy of it and then view the raw message using either the menu option View → View Source or the keyboard shortcut Ctrl + U.

As of Thunderbird 31.5.0 this is still relevant, and my current solution is "File -> Save As -> File" and then pick file type "HTML" which does "what you expect". But, you have to bounce out to another application like Notepad or Firefox (view source) to access the HTML source rather than being able to use the built in Firefox text editor, which is not always the most efficient path to your goal.

All the previous answers (view -> view source, other actions -> view source, and Ctrl-U, which are all the same) do not seem to work, because as Tyler Rick correctly notes they present raw message with mime formatting (as well as message headers). And, in the current version, I don't even find View Source available on drafts. Certainly the "view source" implemented is a powerful feature as well, I just think it was that wrong default choice and should be an advanced option.