This is a trimmed-down version of Micromarkdown.js.
It is smaller, and doesn't support the AJAX/include or tables functionalities.
Here's a simple JSFiddle demo of the parser:
Picomarkdown Demo
License: MIT
Version: 0.1.0
Date: 10.2014
Adjust to suit your preferred module format.
var md = require('picomarkdown');
var html = md.parse('*this* is __easy__ to `use`.');
console.log(html);
All credit for Picomarkdown goes to the author of Micromarkdown.js, on which this library is shamelessly based: Simon Waldherr.