Why do some computer power cables not have ferrite beads? What type is usually used?
A ferrite bead around a cable adds common mode inductance to the cable.  The purpose is to increase the impedance of the cable at high frequencies.  With higher impedance, less power can be radiated or conducted from the cable.

Whether your cable needs a ferrite around it depends on whether you need to reduce the conducted or radiated emissions at high frequencies.  If it is for personal use, then there is little reason to bother.

If you are trying to sell a product, then you have to make sure it conforms to the emissions standards in whatever jurisdiction you offer it for sale in.  In the US, these standards are defined in part 15 of the FCC rules.  In Europe, you generally need to meet CE specifications.