it depends, because if you do round pens, no, they don't need supports.
You can also half bury the bottom course, and that anchors the whole thing. If you bolt them well, just the anchor at the base will hold them in place (no posts).
A post every now and ten isn't a bad idea, though.
I have been thinking of doing something like that (standing tires on edge and bolting them together) but filling the bottoms of the tires with soil and planting in them..perhaps alpines or something that can take the limited amount of soil. That would take care of the standing water=mosquito problem. Actually, even if they are lying down, the sidewalls will collect water. I've used them to hold down tarps over hay bales and was quite surprised how much water finds its way into the tires. Maybe fill them with straw and plant something (potatoes?) in them..to fill them with dirt would be a huge job.