[AChimp]

The laws change depending on the country, but I believe in most cases it is up to immediate family members to make that decision, except in cases where there is a living will that specifies "If I'm brain dead, kill me." Even then, family members can contest the living will, though IMO, they're not doing the brain dead person any favours.

Then again, they're not really doing any harm aside from insisting on occupying valuable hospital space.

When there's no family, I believe that it's up the the doctor.