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.