It really depends on what the cause of the blindness is. In old age people often get impaired vision from a clouding of the lens of the eye called a cataract. This can actually be repaired by surgery that removes the lens and replaces it with a plastic one.
You can see the different causes of blindness here: http://en.wikipedia.org/wiki/Blindness#Causes
Babies that are born blind don’t always have the same cause, as the eyes, the optic nerve that carries signals from the eyes to the brain and parts of the brain itself can all affect sight.
If blindness is caused by damage to the brain areas for vision like the ‘primary visual cortex’ (this is at the very back on the brain) then I don’t think there is currently any way to repair this. However, some people who have damage to this area of the brain and can’t ‘see’ parts of the space in front of them are actually able to detect things where they shouldn’t. This is called ‘blindsight’ and the condition seems to occur because another part of the brain that carries signals from the eyes still works, although blindsight patients aren’t aware of seeing things from these signals. It is a very fascinating disorder.
I think Tim’s answer here is brilliant. And I agree that blindsight is a really fascinating condition.
In some people who’s damage is to their eyes, rather than their brain, you can stimulate some kind of visual response by stimulating the area of the brain involved in vision (the back area of the brain). Although this is not the same as seeing, it can be an amazing experience for someone who is blind. If the brain still functions, in the future there may be some way of giving people artificial eyes which can attach to the visual cortex of the brain and relay visual information to the brain, which the brain could then process as if they were eyes. This would be similar to the way cochlear implants work for deaf people.
Hope this helps, let me know if you’d like more info!