WebMaestro.Fr

Upload the layers of your image, and create a parallax effect !
It works great on smart devices too !
The first step is to create with your favorite picture editing software (Photoshop, GIMP…) an independent image for each ground composing your image. All these layers shall be the same size, and should be in .png format as they are meant to include transparency areas. 
Then, on your post editing page in WordPress, click the Insert Media button, and (the same way you would create a gallery) upload your layers under the Create Parallax item. Reorganise the layers if needed, from the background to the front. 
You can finally configure the animation (calibrate, invert, limit, scalar, friction), and publish !
There is <a href="http://webmaestro.fr/image-parallax-plugin-wordpress/" rel="nofollow ugc">some examples</a> on the plugin page.
It uses <a href="http://wagerfield.github.io/parallax/" rel="nofollow ugc">parallax.js</a> by Matthew Wagerfield.

Image Parallax

Create images with a parallax effect. Upload some layers, configure the animation, and publish !

tommygeorge

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.

Super Simple jQuery Parallax Background

For themes with background images, creates a parallax effect when scrolling. Super simple; no configuration. Just works.

Image Parallax vs Super Simple jQuery Parallax Background