There's a bunch of them, but you'd never want to run hard realtime on a phone or tablet. Hard realtime gives you horrible performance, but excellent latency guarantees. One big thing they do in hard realtime systems is to disable the CPU cache, because caching prevents determinism. It's also essential for performance, but in a hard realtime system performance isn't important.
VxWorks, eCos, ITRON, RTEMS, RTX... There are a plethora of players emphasizing specific features. Outside realtime, various BSDs and then some RT Linux and even still wince.
Free software plays a huge role in this field of course, dating back to the Cygnus days.