Hi, I am in the middle of putting together my first  AR and was wondering what kind of collection of spare parts should I take with me to the range, or have on hand in the event of an emergency?

Spare mags.

spare rifle

lots of spare ammo

I have sent 10s of thousands of rounds downrange in several ar's in the last ten years. I expect this would be considered chump change by some guys but it is a fair amount. The only parts I ever went into my stash for was an extractor spring that I replaced on a used gun I had bought that was not running perfect. Cleaning alone likely would have fixed it but since I had it apart and some extra power extractor springs  on hand I threw one in it.
For range use I don't bother to carry spares other than multiple mags, but I only live 4 miles down th street.
For SHTF there is a lot to recomend a spare bolt group,If the gun starts to act up you yank out the complete bolt and carrier and replace with the spare and you are back in buisness in seconds. then you can find out what is wrong when you have the time and place of your choice.
Any time you start to take anything apart you run the risk of loseing or messing up many small parts and springs. A spring kit is availible (I got a DPMS at midway for 19$?) and a trigger group is a good spare to have. I have replaced most of my triggers with RRNM sets so I of course keep the factory unit for a spare.
Another good spare is the retaining pin that holds the fireing pin,also likely to be lost or buggered.

SHTF?

Extra bolt, firing pin, a couple of extractors with spare springs and pins...  maybe an extra full LPK if you're paranoid or prone to losing things.  Perhaps an extra BCG for the quick change factor...

Thanks a bunch for the input guys. I guess I'll pick up a spring set and try to find a good used BCG for  just in case.