Mostly cell death is controlled by a very complicated series of chemical steps which mark specific cells for death once they have reached the end of their useful life. In this process the death of cells is controlled and only cells which are supposed to die will. When cells die unexpectedly it can be because of infection or injury for example and is called necrosis.
Necrosis can be a very big problem because there is often a large inflammatory response and the dead cells will release potentially dangerous substances into the body which can then lead to further problems. Probably the best known example of necrosis is gangrene which happens when blood supply to a part of the body is reduced, possibly by infection or injury, leading to cell death. Often the only effective way to treat necrosis is to remove the dead tissue surgically.
Like Matt said, cell death is usually a controlled process that happens to cells that are no longer useful to the body. This programmed cell death (also called apoptosis) is really important when the body is developing as an embryo – as Alison mentioned in her lecture, when our hands and feet are developing they are webbed like a duck’s feet! The cells in between our fingers and toes have to go through programmed cell death to make our hands and feet the right shape.
You asked a very interesting question, because programmed cell death can sometimes happen in cells that would still be useful to have in the body, so the cells die when they are not supposed to. This is what causes degenerative diseases.
For example, in Alzheimer’s disease, neurons in the brain die through this process of programmed cell death, causing symptoms like memory loss. Our neurons don’t divide very often once we are adults and the brain has finished developing, so unfortunately we cannot replace the neurons that have died.