I see posts about keeping spare bolts and firing pins in the grip and whatnot.  Do these parts actually break?

You wouldn't like it if they did, and you needed one right then.
If they are your target shooting guns, no big deal.
If they are your homeland security guns, get soare parts.

For rifles that are actually used, trained with, competed with, etc., parts will break.  If you are a casual/recreational shooter, these parts may last your whole life time.  Having a part break and not having a spare can ruin a good range day, competition, etc., so it is always a good idea to keep a minumun number of spare parts on hand.  A complete bolt and firing pin is a good start as the cost of spares is minimal.

What part breaks are common on the AR?

Quoted: What part breaks are common on the AR?

Firing pin is the only thing I have had break.