South Australia actually has quite a few places, where you can camp for free. However in some cases you still need to pay an entrance fee for the attraction or the national park.
Murphys Haystacks

Murphys Haystacks has an honesty box which you can chose to put money in. If you don’t, well then you just get to camp for free.
+ Toilets
% No water or showers
Wave Rock/Pildappa Rock

Wave rock or Pildappa Rock as its called has camping spots all around the rock.
+ Picnic areas
+ Toilet
+ BBQ area
% No showers or water
Talia Caves

At this free campground you have to be self-sufficient.
+ Scenic view by the ocean
% No water, toilets or showers
Wanna Sanddunes

Wanna Sanddunes is located within Lincoln Nationalpark, so you would have to pay an entrance fee. However there is no fee for sleeping in the dunes, so you could give that a try instead of paying for a campsite.
+ Awesome view and secluded feeling
% No toilets, showers or water
Lake Hart

Lake Hart is located on the highway between Cooper Pedy and Port Augusta. This free campground is basically just a rest area along the highway, but its quite nice, since it has a great view and is also a bit secluded from the noise of the cars.
+ Next to a cool saltlake
% No water, toilets or showers
Kimba

You’ve probably seen a picture of the Silo Art in Kimba. Kimba provides a free camping area for all the travellers. The campground is not located by the silo art.
+ Showers
+ Toilets
+ Water
+ Free books in the Women’s toilets
% Nothing beautiful
Lake Gilles

Lake Gilles is just a 30 minutes drive from Kimba. You can camp all around this lake and find a beautiful spot for yourself. Beware of the bees!
+ Secluded feeling by a cool saltlake
% Bees, no showers, no toilets, no water
