As a new home brewer, I've been reading up on posts regarding things that can go wrong during a brew and how to fix them. For example, if I have understood correctly, stuck fermentation may require extra yeast to get things going again. Now, Murphy's law dictates the local brew shop will be closed when/if this happens. I am thinking it might make sense to keep a couple packets of Safale 05 (seems to be a general option for the few kits I've looked into) in the freezer just in case. Are there any other supplies that might make sense to keep an extra one of them around? I'm not thinking glass carboy here simply because of the cost but simple $5 things (airloc) that are just a few bucks that you wouldn't want to wait a week to get from Amazon.
An extra airlock isn't a bad idea, but I'd also recommend having a bucket and some sort of tubing/equipment for a blowoff tube setup. There seem to be a lot of ways people set this up, and it's nice to be able to swap out the airlock for a blowoff tube (I actually have a disassembled airlock with some tubing attached that I keep in a bucket for this purpose). This can also just be a nice starting state for a fermentation if you're at all unsure if you have enough headspace in your fermenter.
As you mentioned, extra yeast is good to have. I think some people use US-05 and others use champagne yeast for this if they really want to be sure that they clear out any remaining fermentable sugars. Or just keep on hand a couple packets whatever the cheapest yeast you can find is.
Many people also recommend having an extra hydrometer since some people seem prone to breaking them, though I haven't really had any problems with this.
Having some extra DME on hand can be useful too, for making yeast starters, priming bottles, making last minute gravity adjustments, or even making a mini batch with some extra hops and yeast.
For kegging it can be nice to have some extra hose clamps and/or keg fittings. And maybe a bit of extra tubing as well.
Also, for what it's worth, it nice to have a thermometer and scale in your kitchen just in case they're useful for brewing (and loads of other things). Buying an extra scale probably isn't necessary, but having a back-up thermometer can be nice, just in case something goes wrong with the one you're using for brewing.