JIRA uses its own plain-text markup syntax, which I don't like as much as Markdown.
Fokke Zandbergen has a great online service for converting between JIRA markup and Markdown, but it's too cumbersome to use this when you are living in JIRA comments.
This will take the Markdown in the clipboard and paste it as JIRA markup whenever you type ";jira".
You can download the macro here.
Update – May 26, 2016: I have added support for multi-level unordered lists – the updated code is below.
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