Which parts on the AR15 are most common to have issues or breakages that will render your weapon useless?
Here is a list of parts most likely to break that you should keep on hand.
Extractor spring insert, Extractor spring, Cam pin, Trigger Spring, Firing pin, 2 Firing pin retaining pins, Safety detent, Extractor pin, Detent Spring, 3 Gas Rings, Disconnector, Hammer Spring. These should go wherever your rifle goes.
You can buy field repair kits for about $31.00
These spare parts should make sure that you are not out of the fight for long if something minor should break.
I also like to have a spare bolt on hand.
Of course the very best spare is another complete rifle, however, although I own several AR15's, I also have spare parts on hand as well... Just in case.