Spare tube: Sometimes, a tube is just too damaged to be patched, or has had a failure such as the valve stem breaking off which isn’t something that can be patched. To save weight and space, I usually keep a lightweight version of the right size tube for my bike. Since one of the first things I do with most bikes that I own is switch them over to heavy-duty thorn resistant tubes, I just take one of the originals and put that in the toolkit.
Many bikes, including older models and track bikes, have bolts attaching the wheels to the frame instead of quick-release levers. If your wheels are bolted on, in most cases you’ll need a 15 mm wrench to remove it. We didn’t test wrenches, because there aren’t that many tiny 15 mm wrenches, but the GearWrench 15mm 12-Point Stubby Combination Wrench is perfect for stuffing into a flat kit and Amazon reviewers seem to think the same. Our experts also recommended the Surly Jethro Tule, but it’s expensive and harder to find.
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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.)
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.
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.