A complete, quality, bolt carrier group with firing pin is always a smart thing to have.
At the very least, a spare bolt, firing pin, and extractor. Extractors are wear items.
I'd recommend a used Colt BCG, or a new Bravo Company or Spikes BCG. All are now built to mil spec and tested thoroughly. The spikes and maybe the Bravo Company have upgraded extractors to handle steel-cased ammo better.
A lot of people will buy an AR off the shelf, like a bushmaster, dpms, stag, S&W, etc, etc, and then replace their BCG with a Spikes or Bravo Co and keep the original bolt carrier group as their spare. If you read the "what goes wrong in a carbine course" thread, a lot of pain is avoided by running quality BCG and having spares for those parts.
I could probably stop right there, but I'll add a few more thoughts.....
If you run illuminated optics, lights, lasers, etc, etc, extra batteries no matter how remote the possibility is that the batts will die. Along with that, any tools needed to adjust your optics or mounts. (i.e. torx/hex wrench, coins, 3/8" wrench etc, etc.) Don't forget the blue loc-tite for when you discover your scope mount was coming loose.
And as with any gun, a bit of oil can do wonders to keep you running. Everyone has their favorite, but a small bottle of oil seems to get jammy guns running again easily. Oil it well before your first trip.
I'd also pack a 20-24" wooden dowel the first few range sessions if you are running steel-cased ammo. Some like to stick in tight chambers. You will know quickly if your gun will run steel ammo. If it does, you can start leaving the dowel at home.
A full lower parts kit should find it's way into your collection at some point too. Say you change your stock, and the little springs that work the safety detent goes flying into the grass......... Good stuff to have. Sucks big time to slap on a new stock on a Friday night, loose your spring, and have to sit at home all weekend when you had planned to hit the range.