Brother, you would freak if you saw my spare parts giant tackle box. I've posted pics of it here before - I think I even had a contest that anyone that could 100% identify everything in it - could have it.
At any rate - cam pins. I didn't see anyone mention cam pins yet. Just one, per frame, will do (small frame AR15, bigger frame .308AR). Like others have said, gas rings, firing pin, firing pin retaining pin, ejector and extractor, with their pins and spring, a bolt (complete) - you break a bolt and you might have to the time to rebuild it right then, if it's a stripped bolt. Even if you have all the stuff to rebuild it, which you should. A gas tube and roll pin for it. Trigger and hammer pin.
If you have spare lower receiver pins and springs, the list of BCG sub-components listed above, a spare recoil system and gas system - you're good. You need the things that will stop your rifle from functioning.