The damage caused by ESD will depend on the component and the quantity of charge dissipated. The components at risk most are semiconductor chips such as processor and memory chips. These chips are found on almost all computer system components from floppy drives to video and sound cards. All are at risk from ESD.
The damage caused to components may be severe enough to cause the component to fail completely. There is also a very high risk of latent failure where the damage is not immediately noticeable but still the device could fail later, either completely or intermittently. ESD damage will at best reduce the working lifetime of the component and at worst cause permanent, immediate failure.