IT depends on the area. Some backpacking areas don't see a lot of people, and you can pretty much camp wherever you want within a few rules - 200 ft from water bodies and streams and trails, an acceptable distance from others (judgement call), and not in restricted areas (some hi-altitude meadows come to mind). Other areas are almost overrun by backpackers so the local oversight agency set limits on how many people can start up a trail each day, where you can camp, and have rules regarding trash and poo disposal (the heavily overused Mt Whitney area in California's Sierra Nevada Mtns is a prime example of this) Check with the local agency running the area (national foest, national park, or the state equivalent of each of those), they usually have an internet site and have the basic regulations/rules on that site.
Like others said above, don't even think of building shelters. A lot of natl forests/state forests and parks prohibit building shelters except in emergencies. Bring a tent or a tarp so as not to disturb the local ecology. Leave the area looking like no one was there.
Also of note: A lot of areas prohibit campfires and have some pretty stiff fines for starting a campfire unless its an emergency situation.