It turns out that these messages are usually of "Content-Type: multipart/related" or "multipart/alternative". The idea is that the same content will be sent out in multiple versions (such as text/plain and text/html) so that your email client can display the preferred format. Unfortunately, I think many of the sites that send out such messages do not have the software configured properly, so that the plain text alternative, which is usually listed as the first alternative, is either blank or corrupted.
You can view the content of these messages by selecting View -> Message -> Next Alternative. This will cycle through the other versions of the message, and (usually) these at least one of the other versions will be readable.

