The most common parts I have seen fail or just plain wear out are the bolt parts. You can put your own spare parts together or companies like Rock River Arms have bolt rebuild kits already assembled.
Upper Receiver Parts (Part#AR3258)
In addition as Model 5 already mentioned, keep several of the firing pin retaining pins, they are easily lost during cleaning and once the legs start to spread apart they become difficult to reinsert. They are cheap.

Depending on the trigger that your rifle has, you may want to have spare, hammer, trigger and disconnector springs. There is not much else that you need. Most everything else would involve a major failure. I am working on putting together an entire complete bolt & bolt carrier for each of my AR's (13) that include several different calibers.