It has annoyed me for some time that parallax sites does not work on mobile devices (or rather, people that make parallax websites does make them work on mobile). But at a workshop at @ValtechSweden we came over stellar.js which is a script that together with iScroll4 will make this work on mobile devices as well. Of course, it is not just a matter of using the script, you will need to apply some responsive magic to make it work, but it is actually quite promising. I set up a very simple demo here: http://andmag.se/parallax.
WARNING: Kids, please try this at home, but think twice before applying it at work. Parallax effects may cause enthusiastic clients, but very sad and dizzy end users. And kittens may die.