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.
Keychain style flashlight or headlamp, LED type, not incandescent: The keychain style is tiny and lightweight, the headlamp style is a bit bulkier but easier to use. You can get these for a couple of bucks or less at the local big box hardware store. The LED ones are lighter, more durable and last considerably longer. Very useful if you need to make a repair after dark! I keep a keychain style one as a backup as I normally have a headlamp in my backpack.
Basic first aid supplies: A few bandages of varying sizes. 6 Aspirin, or other OTC painkiller of choice. A few alcohol pads in sealed foil packs, useful for cleaning grease off grease and grit off of the bike, and also cleaning cuts on yourself if you take a spill. 1 day supply of any prescription drugs you need to take regularly. Wrap these up in tinfoil and tuck away. It might just save your day.
Brakes come in a variety of designs depending on the age and style of your bike. Rim brakes offer more modulation but have less stopping power, so are more suited to riding on the roads. Disc brakes can provide huge amounts of stopping power so are best suited to off road riding, although ‘V’ rim brakes are also well suited to mountain biking. All brakes use a friction system to stop the movement of the wheel, so regular checks of the contact pads should form part of your regular cycle maintenance.