With a power surge or spike, if the PSU doesn't react quickly enough or doesn't have sufficient protective features, you could lose an entire system. If the PSU itself suffers a catastrophic failure, again whole system loss is possible. You guard against these by using a good quality surge protector or uninterruptible power supply (UPS) and a high quality PSU.
With a short, the damage is likely to be much more limited. Having said that, almost everything in a computer connects directly to the motherboard which acts as the central hub for power and communication between components, so if a component experiences an electrical failure, it's possible for the damage to extend to the motherboard or a part of the motherboard. Some parts are more important than others - if you burn out a fan header, you can work around that; if you burn out your front panel header, you'll need to replace the mobo. It's possible for the damage to extend from a component to the mobo and then to another component, but that's not very common. If computer designs allowed that type of event as a norm, you'd have computers burning out all over the place and mega liability lawsuits. Normally if a component dies or shorts out, it dies by itself.
Again, with a good quality surge protector, a high quality PSU, and a moderate amount of care and maintenance, you shouldn't need to worry about it.