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.
Broadly speaking there are two major wheel sizes – 700c for road bikes and 26 inch off-road wheels. However there are a whole variety of older, less common wheel sizes and of course fold up bikes have much smaller wheels altogether. Repairing a puncture is not an emergency! It’s a basic procedure that every cyclist should be able to to perform, but doing it correctly involves more steps than many people realise. Wheel building is often seen as the most artful skill in bicycle maintenance, and separates the professionals from the amateurs but that doesn’t mean you should consider it out of reach. Truing a slightly misaligned wheel is a cycle maintenance job that almost any cyclist can perform.