Super Simple jQuery Parallax Background enables a parallax effect with your theme’s background image. Just set a background image in your theme’s “customize” options (optionally setting it to “fixed” position) and activate this plugin. Done. “It just works.”
It relies on jQuery, which comes with WordPress and is probably built into your theme. Tested and works with the “Twenty Twelve” theme out of the box.
Looks best with seamlessly-tiling background images.