We always call them 'way-sides' where I come from in Wisconsin, which may be short for 'way-side rest stop' - they are much as Vicky described them, although minus the phone. Usually on a road other than an interstate, sometimes with a picnic table or two, sometimes with a pit toilet, sometimes just a place to pull over out of the traffic, not even paved...
I've never heard those other American terms for it...