What about images, links? Formatted text like bold or underline?

I also prefer plain text, but in most of my emails I talk about technical stuff, or I send transactional emails that require actions, in which case showing buttons is a much better user experience than plain text.

Embedded images aren't really compatible with Markdown. They just aren't. (Oh, syntax for it is defined, all right (in Gruber's implementation, even). But it doesn't really cohere with the rest of Markdown—in the way that Markdown is an opinionated way of formatting your plain text documents so that they can optionally be mechanically translated for typesetting systems that have richer formatting options.)

Any serious Markdown-to-email should probably look like this:

Markdown, formatted as readable plain text (i.e., not the way that GitHub encourages people to treat it as just alternative "lightweight" markup syntax that you just tickle differently when you want the end result to show up how you want; Markdown is supposed to be readable in raw form) and sent as plain text email, no HTML or multipart/alternative in sight

+

A convention of including a special header (or trailer in the message body) that denotes to the mail client, "This is plain text, but it happens to be valid Markdown, and the author wishes to express their intent that it be treated as such, with richer formatting for the recipient (to be overridden at the recipient's desire)."

I don’t want buttons in my emails.