Both the Missouri Ozarks and the Ozark Highland Trail have some great camping opportunities. They both allow camping along the trail and have some official campsites, if you prefer.
Because the Ozarks covers such a large area, it's a good idea to look into the climate where you're going to be camping and plan accordingly. Depending on where and when you go, you may need to prepare for cold weather, walking and camping near riverways, or making your way through wilderness. Elevation in the Ozarks varies quite a bit from mountains to valleys. That means that no matter what time of year, you should prepare for changes in temperature.
On the Missouri Ozark Trail, the rules about camping vary by section. The Ozark Trail Association maintains a page with trail conditions, and you can also click on each section to get more information about that leg of the trail, including camping rules and where to find campsites. For example, the Taum Sauk section has a couple of campgrounds, but if you're planning to camp elsewhere, you must make camp 100 feet (30.5 meters) from the trail [source: Ozark Trail Association]. The Ozark National Scenic Riverways have quite a few campsites, and you can find campsite infomation through the National Park Service.
The Ozark Highland Trail is very camping-friendly. You can pretty much camp wherever you want along the trail, and there are 18 public campgrounds along the trail, if you prefer less primitive camping conditions [source: Ozark Highlands Trail Association]. If pitching a tent isn't your thing, you might want to plan your trip around White Mountain Rock, where you can stay in a cabin instead.