We would probably all agree that the most important components of your bike are either the frame or wheels. Some may also argue that even more important is the saddle and handlebars, which define your riding comfort. But what about those hidden parts that you normally don't see, and which are absolutely critical for your bicycle to function properly? Here are the 3 most important invisible components of your bike:
Cables are hidden inside housings (sometimes not completely) and you normally don't pay attention to them as long as they operate your brakes and derailleurs. But keeping cables clean and damage-free is critical if you don't want to suddenly end up brakeless on the long downhill ending at the busy street. Or if you don't want to lose your gears, which happened to me once when the shifter cable for my 3-speed hub broke unexpectedly, forcing me to limp slowly (in the 1st gear) to the nearest bike store to seek a replacement.
Check the cables periodically to make sure they don't have any individual wires broken. That's how the bigger problems start. It's also a good idea to oil cables inside the housings a little. If you ride a lot in wet conditions (rain, mud) you should seriously consider upgrading to Teflon-coated cables and housings with insulated ferrules). Jagwire and Gore make good ones. But even if you generally avoid rain, it may be worth choosing insulated housings for your cables (or at least lubricate them periodically), should you ride a lot in winter. Frozen cables can be a serious problem.
If you don't remember hubs with cup-and-cone bearings that required two wrenches to carefully adjust each bearing cone, you're still a kid. Fortunately, these old-fashioned hubs are pretty much gone today (unless you still ride an oldie from the 80's). We have sealed industrial bearings in all modern hubs, bottom brackets and headsets right now and these require much less wrenching than old cones but still some care. Good quality hubs will last many years unless you spend many miles in muck and mud. It is still a good idea to check on the wear of the bearings once a while and lubricate them when necessary. Should you feel any play in your headset, cranks or hubs, it's definitely time to check on bearings condition.
Ok, air is not really a bicycle component but without it you definitely wouldn't go too far. From all the parts on your bike this is the one you literally can't see but it may be the most important one. For decades, it used to be quite simple. Mountain bikers and cyclo-cross racers would go for the lowest air pressure their tires can handle without risking a pinch flat. Road cyclists would go for the highest pressure their tires can handle without risking a blow out. Now that we are smarter and we have more tire options than ever, it isn't that simple anymore.
The current trend to move towards wider tires changes things quite a bit. Less air pressure would mean more traction and a more comfortable ride, provided that tires on your bikes are not made of a rock-hard rubber. For mountain bikers the biggest change would happen once they try a fat bike or put tires at least 3.0" wide on their 29ers. Running these at high pressure is a mistake.
Road cyclists should still keep the pressure high in their 23-25mm tires but once you start riding with 32-38mm tires on your road bike (provided it has enough clearance to fit them) forget about inflating them to whatever maximum pressure manufacturer specified. I currently ride at only 30/35 psi (front/rear) in my 35mm wide tires and I'm very happy with this setup.
Unless you ride on a perfectly smooth velodrome, small bumps are better damped by a low pressure, wider tire (that simply deflects and rolls over debris) instead of a high pressure, skinny one (that must jump over each small rock).