I've tried to keep the answers as short as practical while still providing the required information. If you have anything to add, tell me about it. For more detail, refer to this thread.
Q1. How do you choose a fan, basically?
A1. As a compromise between high airflow, small size, and low noise.
Q2. What part of the fan produces the most noise?
A2. At moderate to high speeds, the tone from the impeller usually dominates. Bearings in good condition are only responsible for a small part of the overall fan noise (except with ball bearings at very low speeds).
Q3. How do I determine the pitch of the tone?
A3. Frequency in Hz = (RPM/60)*N where N is the number of blades
Q4. What effect will obstructions have on the fan noise?
A4. Usually a small one if they're placed "behind" the fan (by which I mean on the side it blows at). But if they're in "front" of it (the side it sucks from), the noise will increase dramatically, and you may end up reducing the speed to compensate. Mounting a safety grille to the "front" of the fan will (not might) cause that.
Q5. How do I know which way the fan blows air?
A5. There should be a pair of arrows on the fan frame. One indicates the rotation direction and the other indicates the airflow direction.
Q6. What is the effect of changing the rotation speed?
A6. The flow in free air is correlated directly to rotation speed, and the pressure is correlated to the square of rotation speed. As for noise…let's just say you don't want to run the fan faster than truly necessary.
Q7. Are there big differences between the performance characteristics of different manufacturers' fans or are they all largely similar?
A7. Similar fans usually provide similar performance. Reliability is the primary basis on which manufacturer (and model) to choose.
Q8. Are the big top-mounted PSU fans really a better configuration? It looks like a lot of compromises they have to make…
A8. There are indeed a lot of compromises, and given similar ventilation in both units (there are many 80mm-fan units with awful ventilation), it is ultimately worse than the traditional rear-mounted 80mm fan.
Q9. Can you change the fan speed by altering the input voltage?
A9. Yes, to a degree, but if you go too low it won't start, and if you go too high you'll destroy it.
Q10. How do sleeve bearings compare with ball bearings?
A10. Sleeve bearings in good condition are quieter, but should only be mounted with the shaft horizontal and the lubrication is critical. Ball bearings can run in any orientation but are more vulnerable to shock. As for fans with one ball bearing and a sleeve bearing, they would seem to be merely the worst of both worlds (if not even worse!).
Q11. What are the maximum rotation speeds you'd recommend to stay at an acceptable sound level?
A11. Outside of PSUs (where wind noise often becomes the elephant in the room) — 6000RPM for 40mm; 4800RPM for 50mm; 3600RPM for 60mm; 2700RPM for 80mm; 2100RPM for 92mm; 1600RPM for 120mm — given no obstructions in front of the fan. I wouldn't really call those quiet, though — that will require significantly lower speeds again.
Q12. Are thicker fans quieter than thinner ones?
A12. Sometimes they are, sometimes they aren't. My best advice would be to look at the specs. However, a notable example of the thicker fans not being quieter is when comparing 120mm fans, where the 38mm thick models are usually (if not always) designed to be powerful, so whenever quietness is desired, use the 25mm thick versions (or the 30mm thick Phanteks PH‑F120T30).
Q13. How much power do these fans draw?
A13. At rotation speeds providing an acceptable noise level in PCs, they usually draw less than 2W each.
Q14. What if you use two fans in series or parallel? (airflow-wise)
A14. If the fans are identical, running them in parallel will double the flow in free air, but the static pressure will remain unchanged. Running them in series will not change the free-air flow, but will double the static pressure. The parallel fans will be up to 6dB louder than an individual (so a single large fan would be preferable), but far quieter than a similar fan at double the speed would be.
Q15. Is there any benefit in changing the original thermal pads out for thermal paste?
A15. Not if you're dealing with the modern phase-change pads.
Q16. How does copper compare to aluminium as a heatsink material?
A16. Copper has close to double the thermal conductivity of aluminium, but is more expensive and much heavier; so is justified mainly in places with high heat density. (Integral heatspreaders are usually plated copper.) Ultimately, though, it's not about what material is used — it's how the heatsink is designed.
Q17. Do heatsinks perform better with the fan blowing down or sucking upward?
A17. It's a bit hard to say, but consider first that fans with obstructions directly in front make much more noise. That probably explains why it's standard to have the fan blowing down.
