The bicycle is an astonishingly reliable bit of kit; I ride up to 10,000 miles each year and seldom experience anything worse than a puncture. Furthermore, when something does go wrong, it is almost always fixable at the roadside provided you carry a small but well chosen set of bits and bobs.
There is an old saying that you can fix everything using just gaffer tape and WD40 – basically if it moves and shouldn’t you use gaffer tape and if it doesn’t move but should you use WD40. In reality it is a bit more complex. For what it’s worth, here is what I carry when I am touring (or riding sweep on a cycling holiday):