A spare AR doesn't hurt like any of your firearms it's always good to have extras. But for replacement parts I'd say it depends on what you can afford and what your plans are. Ban and shtf bugging out are always the same. Afterall if you're bugging out with the pack on your back, rifle in hand and a sidearm, you can't afford to carry extra weight you're very unlikely to need. In that aspect a spare complete bolt is good enough to me. You should always try to keep your bugout rifle in top shape with the wear off the parts in my opinion so they last you as long as possible when you've bugged out and have to rely on them with slim chances of replacement.
For ban and long term shtf, bugging in, everything is certainly good, but a complete bolt carrier group, buffer spring(or 2), low parts kits, sight post, barrel, barrel nut and the tools to replace the barrel are a good place to start. That's if your using a DI AR, if you're into piston AR's as I have been for a long time now and not using DI's anymore, than you need to have the replacement proprietary parts besides.
Everything else you can live with. For example some people stock up on extra barrels but when are you ever going to fire 100000 rounds to wear down the barrel to the point it doesnt shoot straight? Seriously when?
What else to get spares of? Maybe some of the pins and springs as they might get lost or get rusted out or weaken (Spring). These are cheap. They usually comes in a kit with all of them in a set.
Lastly some other nutjobs out there keep spares of lower receivers. There is no point of keeping an extra receiver or two. If you are going to get an extra receiver might as well go buy an extra gun since the reciever is serial number and are registed under your name so might as well be another AR.
So bottom line is buy extra firing pin and maybe a set of the small stuff like pins and springs. Everything else will not wear down enough for you to worry in your lifetime and perhaps your kids lifetime.
Rather than replacement parts I focus on number have more complete weapons with interchangeable parts.
I have also start going with Gas piston AR's they hold up better stay clean and the uppers and lowers are interchangeable with other AR's