GitHub Gist supports MarkDown.
On the homepage enter your code, and select "Markdown" from the language list. You can publish your gist publicly (shows up in results of search engines) secretly (doesn't show up in search results, but the gist is still accessible for everyone who has the link).
Here's a basic example: gist.github.com/basilevs/de72b93d72a80d078f29.
For more information about creating gists in general, refer to Creating gists - User Documentation
Rentry is fast and simple and supports MarkDown.
wrttn.me allows for embeddable content (such as YouTube videos) and provides an API for you to grab your content in plain HTML.
Socrates is run off firebase and running since 2012 it's almost as minimalist as it gets... it's beautiful and doesn't get in your way
Markdown.press is probably what you're looking for.