A pair of disposable latex gloves:  Not absolutely necessary, but good for keeping grease and grime off your hands during a repair.  Also, nice to have in an emergency when it starts raining and the temperature drops 20 degrees and you don’t have a pair of regular gloves.   Just keeping your hands dry and the wind from directly blowing on them makes a huge difference in comfort.
We spoke to a broad spectrum of cyclists—from a pro racer to a bike messenger turned mechanic to a touring cyclist who has logged thousands of miles throughout Europe—to find out what items they find indispensable. We sorted through 40 tire levers, almost 30 different kinds of patches, 120 different hand pumps, and 57 seat bags before we narrowed our choices for testing. And then we changed and patched tires more than 50 times, using four different bikes, five different wheels, six different tires, and almost 10 different sizes of tubes. After 96 hours of combined testing, we agree these essentials are some of the best you can buy.
If you’re going to use the chain whip you just made, you’ll also need a way to get that cassette off. A lockring remover is a must-have; unless you use one of the shady removal methods I’ve seen on the internet—which I wouldn’t necessarily recommend unless you don’t care much about the condition of the wheel after you use them. I recommend Park Tool’s iterations here that cost about $6, but you’ll need to buy the specific one for your brand/type of cassette. (By the way, I’m assuming you already have an adjustable wrench laying around somewhere to use with this tool. If you don’t, well, you’ll need one of those too.)
Modern bottom brackets use a sealed bearing type construction that keeps water and debris locked out, so they seldom go wrong. Maintenance is impossible so they need replacing when they do wear out. Older style cup bottom brackets need to be re-greased every now and again, and occasionally will need to have their bearings replaced. There are a lot more teeth on the chainring cogs than those on the rear cassette, so need changing less regularly. Cranks usually a solid one piece construction so there is not much to go wrong.