Electrostatic Discharge is a danger to all electronic components within a PC.
The actual incidence of components being damaged by ESD is relatively low. However, it's important to take precautions when handling electronic components.
Wear an Anti-Static Wrist Strap. This will earth you, ensuring you don't carry a significant static charge.
You can also regularly touch earthed objects in your home, for a similar effect. Most household radiators are earthed, for example. Regularly touching the metal of your PC's case can also help to reduce your static charge.
Use an Anti-Static Mat when working on components. That will help keep them isolated from static charge.
Avoid rugs, carpets and fabric surfaces if you can. Not only do they help build your static charge but also contain lots of dust, grit and fibres which can clog components.
Overall, as long as you ensure you're earthed (repeatedly, if possible) while working with electronic components, your risk of ESD will be very low. You can reduce it to almost nothing by wearing an Anti-Static Wrist Strap and using an Anti-Static Mat.