So you have been looking around reading reviews, watching YouTube and you are pretty confused with regard to CPU coolers.
What's all the fuss about? Simply put, the hotter the CPU runs the shorter its lifespan will be. One should not be led astray by anyone talking about "safe" temperatures. Your CPU will die at some point as the heat generated by it burns it up, it is the coolers job to drag out that inevitability. There is also no "safe overclocking". A CPU with a temperature of 48 degrees Celsius will last longer than one running at 60 degrees. Anyone telling you otherwise is just - how do I put this politely - lying. There is an exception (see "Silicon Lottery" below).
There is something known as "The Silicon Lottery" which means that your CPU will be randomly more or less resistant to failure (heat death). If you do overclock then one CPU may run stably at a certain speed whereas another will just crash. There is no way of telling short of actually using the CPU if you are a winner or a loser in this lottery. You also cannot send a CPU back the manufacturer which will not run stably at even a mild overclock because technically you are running it outside the manufacturers specification.
If you have an Intel CPU then the cheapest way to knock a few degrees Celsius off the CPU temperature is to turn off HyperThreading in the BIOS.
There are two kinds of coolers and those can be split into two general categories:
1) Air Coolers
a) Stock Coolers
b) Third Party Air Coolers
2) Water Coolers
a) Custom Parts Water Coolers, Liquid Nitrogen
b) AIO (All In One) Water Coolers.
The easiest ones to discuss are those falling into the category 1a, the Stock Coolers. These are the ones you will get with your CPU when you buy it. The only thing that can be said about them is, "Better than nothing, but not by a lot". In other words they are garbage and should be consigned to the bin at the earliest possible opportunity. From my own recent experience, I bought an AMD A8-5600k processor for my NAS and I put the stock cooler that came with it onto it to see how it would perform before putting a real cooler on it.
I booted up the system, started the hardware monitor to check the CPU temperature then I started Prime95 to put the CPU under load. Within seconds after starting Prime95 the CPU temperature shot up to 62 degrees Celsius, which is totally unacceptable and I stopped the testing immediately so as not to damage the CPU.
The next easiest to discuss would be the ones fitting into the category 2a or "Custom Parts Water Coolers". For this solution you have to buy all the pumps, radiators, reservoirs, tubes, joints etc. yourself and put it all together. These will give you the greatest cooling of your CPU if you have done it right; however they do have major drawbacks:
1) You will have to permanently monitor the system because they are prone to failure and leaks.
2) You will have to run all kinds of routine maintenance on them from checking the fill level of the coolant to making sure that all the joints are tight and not leaking, check for algae.
3) It is exorbitantly expensive
4) You will have to sacrifice a significant portion of the expandability of your chassis to the components of the cooling subsystem (coolant reservoirs)
5) They are only as efficacious as the builders ability to construct the complete system.
6) No warranty and dubious reliability. This solution has a VERY limited field of application (especially Liquid Nitrogen which has the added downside of being extremely dangerous if the LN is handled incorrectly).
The next two, 1b "Third Party Air Coolers" and 2b "AIO (All In One) Water Coolers" are the ones that the overwhelming majority of people will choose from. This is also the portion of the post where I will get the most grief.
Let's start off with Third Party Air Coolers. These range from only slightly better than the stock coolers but with advantages like having a smaller dimension. The one thing which can generally be said is that the lighter (in weight) the cooler is, the worse the cooling performance will be. These types of coolers also are, if one is not looking at overclocking, relatively cheap and one can buy one which will fit any kind of chassis one might choose to put the system into. The cooling performance ranges from good enough to great. The "great" will depend on the size of your chassis and your wallet.
How well an air cooler performs is heavily dependant on things other than the design or efficiency of the cooler itself. Essentially what the air cooler does is that it takes heat away from your CPU and dumps it into your case. It is up to the case ventilation to get rid of that heat. In a poorly ventilated case essentially what happens is that warmer and warmer air is recycled and used to "cool" the fins of the air cooler. The other thing is that a higher ambient temperature within the case will also effect the cooling of other components on the motherboard or the graphics adapter.
Then there is the elephant in the room - literally. To achieve the best cooling of the CPU air coolers have to be massive. All their weight is supported by the motherboard and generally they are oriented horizontally to the vertical alignment of the motherboard. This means that if you are moving your system and you drop it then there is a chance that the cooler will break the motherboard. This is apart from the permanent strain the weight of the cooler puts on the motherboard.
Then there is the design of the cooler itself, or rather the mounting system the manufacturers choose. These range from very easy and well thought out to the feeling that the manufacturers of the cooler are bloody-minded sadists hell bent on making your life a misery. Then there are the coolers which have a clip on system for the fans, however if the clips ever spring open for some reason there is a good chance they will short-circuit your graphics card.
Another thing to take into account is whether or not the components UNDER the CPU cooler will get any ventilation or that it effectively insulates the capacitors, VRMs around the CPU from any airflow which might cool them. If a capacitor blows due to excessive heating then it is game over for your motherboard.
If you are going to choose an air cooler for the CPU then you will have to plan the choice of things like RAM with regard to that choice. In many cases RAM slots will be blocked to anything other than low profile RAM. So you could end up having bought the cooler, bought your RAM and end up not being able to put your system together. Another scenario could be that you have bought the components and although the RAM fits, you won't be able to put the side panel onto the chassis because of the height of the cooler.
Personally I would say that if you are considering an air cooler then the gold standard against which you should judge the competition are the Noctua series of coolers. As I have tried to point out, air cooler benchmarks with regard to how well they cool the CPU are not the entire story - by a very long shot.
Last but not least we come to 2b "AIO (All In One) Water Coolers". These kind of coolers have a small footprint on the CPU itself and remove the heat via the liquid to a radiator to be disposed of as you see fit. The main advantage of the water cooler in my estimation is that the weight of the business end is taken up by a component of the system which is specifically designed to take the stress of the weight, namely the chassis itself - if you drop your system then you might dent your chassis, but you are unlikely to destroy your motherboard. No air cooler other than the highest end ones even come close to giving the cooling performance of a water cooler. The highest end air coolers are also more expensive than a water cooler offering the same performance.
The one thing one thinks about with regard to water coolers is "leaks". This possibility has been pretty much eliminated and I have not heard of any such failure - although I am sure such a thing has occurred.
So the choice is a no-brainer right?
Wrong.
Water coolers are expensive and if you only need something which is good enough or have a processor and system which is energy efficient then it is hard to justify the expense of a water cooler. Even though mounting the radiator to the chassis is the best place for the business end of any cooler to be there are many systems where there is just not enough room to do so. If you want to build a system as small as possible then this will be a deal breaker with regard to a water cooler.
If the pump on the water cooler fails then you will not be able to repair it yourself. With an air cooler, if a fan fails then it is very simple and relatively cheap to replace it and restore the cooler to its former glory.
The other problem one has with regard to water coolers is the tubes taking the liquid from and to the pump. Even if you do have a spot to attach the radiator to the chassis you might not be able to get the tubes to cooperate. Jamming the water cooler into your chassis and placing stress on the joints where the tubes connect to the radiator or the pump is a recipe for disaster if even one of those joints ever give and a leak occurs. If you kink the tubes on the water cooler then the coolant will not be able to circulate and your temperatures will shoot up.
I have tried to be as fair as I can with regard to the choices one has with regard to cooling a CPU and I hope this doesn't disintegrate into a series of fanboy rants.