..Fans inside computers; that is, not fanatical computer users.

If your fans aren’t working correctly inside your computer then you’ll likely have problems: The first and main one of those will probably be overheating:

There’s probably a "chassis fan" on the back of your computer: This fan sucks hot air out of the case. The hot air rises from the components, which get hot and heat the air around them. If heat builds up in the case then the components get even hotter. – The chassis fan helps to prevent this from happening.

You might also have an "intake fan" behind the front panel of your computer, or perhaps on the side panel of the case, or both. Some cases have a side-panel fan built-in when they’re manufactured. Intake fans assist the chassis fan by blowing air of room-temperature into the case, where it circulates around the components, picking up heat, and then being blown out again by the chassis fan(s).

These aren’t the most important fans though. A lower-powered computer can often work fairly well without any intake fan. Some can operate satisfactorily without a chassis fan, or both in some cases. (Though I recommend always having a chassis fan if at all possible.)

The most important fans, usually a necessity, are the "CPU fan", and the "PSU fan":

The CPU fan is usually located on top of, or adjacent to, the large heatsink attached to your computer’s CPU or processor. These two components are collectively known as the "CPU cooler". Their joint function is to prevent the processor from overheating. Without either you’ll be lucky if your computer gets a chance to boot up before its processor overheats. Most processors these days include a thermal shutdown mechanism, where if the processor chip gets too hot it senses this and shuts itself down so that it doesn’t "fry" itself.

If the fan on a CPU cooler fails then although the heatsink portion of the cooler continues to conduct heat away from the processor, once the heatsink reaches thermal equilibrium with the processor there’s nowhere for the heat to go, and the processor consequently shuts down or fries. The fan blows air onto the heatsink which removes the hot air from between its fins and thus most if not all of the heat dissipates into the air inside the case; which can then be evacuated from the case via the chassis fan.

The PSU fan is normally located within the computer’s power supply unit itself. This is normally located at the top of the case at the back. Its function is to draw coolant air from inside the computer’s case, across the internal components – which get very hot with all the wattages flowing through them, and to eject it out the back of the case into the atmosphere of the room. If it fails you might smell an acrid stench first as the PSU’s components begin to fry themselves (Maybe giving off smoke.); soon after which the power supply unit will almost definitely fail; possibly with associated fireworks.

In a few cases there may be another critical fan; that being the "chipset fan": The SiS chipset on the Shuttle SS21T motherboard, for instance, requires one. The chipset fan works on a similar principle to the CPU fan; though the availability of thermal shutdown might vary between chipsets. (?) You may also find a "GPU fan" attached to a large heatsink on your graphics card if you have one fitted: This also works in much the same way as a CPU fan.

We’ve now covered pretty much every type of fan you’ll find inside a computer, apart from the tiny fans inside HDD bays, perhaps. Now we know what they are and what they do, you’ll understand why they have to be maintained.

Air is full of dust and vapours. Lots of air passes through your computer. therefore we can assume that lots of dust and vapours also pass through your computer. It’s like a vacuum cleaner: It sucks in air and expels air, except that your computer’s not intended to remove the dist and dirt from the air. Nevertheless it does do that to a certain extent: Where does the dust and dirt it removes from the air end up? Mainly on and around the fans and between the fins of heatsinks.

That’s not good: A heatsink that has the air passage between its fins blocked by debris can’t work efficiently. A fan that’s spinning in dirt is slowed down by friction with the dirt and by the weight of dirt sticking to its blades due to the adhesive effect of accumulated condensed vapours. If a heatsink can’t work properly and the fan that’s supposed to be keeping it cool can’t spin its blades fast enough then heat builds up because it’s not being removed properly: Result = component(s) overheat and shutdown and/or fry.

Your computer itself might notice that it’s getting rather warm inside, and could display a message such as "System fan error: Check system fan." That’s probably a warning that something’s about to fry or to shut down. OK so which fan is the system fan? It’s not specific; but all or any of them could be at fault. The first ones to look at are the important fans; the CPU fan first. The exercise: Clean it. if necessary and you have the expertise, close down and unplug the computer, remove the entire CPU cooler unit from the processor, and clean it thoroughly. If possible separate the fan from the heatsink and clean the spaces between the fins. Clean the fan; its blades and its bearing. – A tiny 500ul drop of hi-grade lubricating oil may be of use when applied to the bearings of some fans such as sleeve-bearing fans, but usually a clean is all it needs.

If you’ve not removed a CPU cooler before I suggest that you ask someone who has to do it for you, as you’ll need to clean off and reapply the heat-conducting grease between the processor and the cooler on reassembly and refitting: If you don’t do this there is a good chance the processor will overheat due to insubstantial heat conduction to the cooler.

Having done that, clean the GPU fan if you have a graphics-card fitted, (It may be difficult to remove the heatsink, so just do your best at cleaning the fan without disassembling the graphics card.) and the chipset fan if one is fitted. I’d also recommend removing, cleaning, and refitting any intake and chassis fans at the same time. Also use compressed air to blow out any dust in the computer’s case and on the motherboard. You can buy cans of compressed air for this purpose from most computer retailers.

Whether or not your computer is warning you of a fan error; I suggest doing this operation at least every couple of years at least.

We haven’t attended to the PSU fan. This fan is probably inside the PSU itself. Trust me it’s not a good idea to open up a PSU, especially not long after it’s been in operation: There are potentially lethal charges stored within the capacitors inside; and even if you avoid the capacitors themselves there’s always the risk of a triggered electromotive-induction shock through discharging a capacitor through a low-resistance inductor. If you need to clean the PSU fan I suggest unless you know exactly what you’re doing, you get someone who does to do it for you, or maybe even replace the PSU if your existing unit is more than a few years old. (If it’s an old AT-model PSU then I suggest that you get a new computer: You’re probably suffering from geriatric computeritis. (Using an ancient substandard computer.))

Clean fans = healthy computer.