A noisy computer can be a real distraction in the workplace and at home. If there are multiple computers in the same room then the offending noise can reach intolerable levels.
There are several steps you can take to mitigate this noise.
1) Clean your computer case fans. If you computer is struggling to stay cool then the fans will spin faster and generate more noise. Simply cleaning some of the accumulated dust out of the case can help reduce noise.
2) Replace your case. Cheap cases used for pre-built computers are usually made of steel and are not very big. Upgrading a computer case, both in size, and quality of materials can help reduce noise. With improved airflow and higher quality materials (to improve heat dissipation), fans do not have to increase in speed to cool components.
3) Replace your case fans. When you buy a pre-built computer it is likely that the cooling fans will be of inferior build quality. There are a wide range of upgraded fans available to retrofit to your computer. Some have improved bearings and alternate fan blade designs to help reduce noise. If you replace your case you also have the opportunity to install larger, slower moving fans which which can reduce noise.
4) Install rubber mounts and washers. Fans and components with moving parts (hard drives) create vibrations. These vibrations travel through the case and create noise. It is possible to add rubber mounts and washers between fixings of fans and components to help reduce the transmission of these vibrations through the case.
5) Install sound deadening materials. If your computer has sufficient airflow you can install acoustic material to the inside of your computer case. This material simply absorbs sounds and reduces vibrations from case side panels.
6) Upgrade your hard drive. Replacing old hard drives with new solid state hard drives (which contain no moving parts) can dramatically reduce noise. They also have the benefit of increasing computer start-up times and computer responsiveness when opening programs.