This is a subset usually referred to as dispersed camping. IME, this is usually the case in US national forests (in fact, I think the rule is that it is allowed by default).
There are a number of parks (including most US national parks) that only allow backcountry camping at designated sites (which may or may not have the amenities described by the GP).
OK. I've only formally backcountry camped in Arches (mile from any trail - no amenities or sign of previous camping where we were), Yosemite (we quietly camped on top of Clouds Rest so obviously no amenities), Joshua Tree (off trail, random spot with amenities), Canyonlands (Needles in a designated spot but no facilities just a marker, and Maze in a random spot with no indication of previous camping), and a few monuments/areas (Coyote and Buckskin Gulch, etc).
There are a number of parks (including most US national parks) that only allow backcountry camping at designated sites (which may or may not have the amenities described by the GP).