Many people with whom I regularly correspond know that I have a strong preference against mail in "pure" HTML format. Here are my reasons, along with recommended alternatives.

1. Spammers can hide tiny images: just a single pixel, small enough that your eye would likely miss it anyway, and the more insidious ones are the same color as the background. The URLs provided for your mail reader to fetch these images can contain encoded data which spammers can use to confirm your identity. I.e., each message they send can contain a slightly different URL, and when a mail reader fetches an image, it serves as confirmation for the spammers that the address corresponding to that particular URL is "live". This will in turn increase the likeliness of getting even more spam.
2. Not all mail readers handle HTML well. Most modern mail readers do, especially those with a GUI, but many older mail readers, especially those which are screen-based, handle HTML badly or not at all. Some people may use a GUI mail reader at work but a screen-based one at home or when traveling.
3. HTML takes up more bandwidth than plain text. Although this is not an issue in many environments (such as a high-speed LAN), in other environments (such a when traveling and stuck with a low-speed dial-up line) the extra bandwidth can be quite inconvenient.

The ideal alternative, when possible, is simply to send plain text, as it is sufficient for the vast majority of e-mail conversations.

When richer mark-up is needed, however, most mail programs which can generate HTML can also generate mixed text and HTML: the message's primary MIME type is multipart/alternative, with the first part being text/plain and the second part being text/html. Conforming mail readers will display HTML if they understand it, or plain text if they don't grok HTML (unless the user has configured it to display plain text by default).

For the curious, I use exmh at work and home but nmh (the CLI-based mail reading set of programs on which exmh is based) when on the road or in any other low-bandwidth environment. Exmh can display HTML, but it is much slower than displaying plain text, and not all constructs are well supported. I have mine configured to display plain text by default for multipart/alternative messages. I also have SpamAssassin configured to score "pure" HTML mail very highly, as the vast majority of such mail which I receive is indeed spam.