Why are downed power lines dangerous? A friend of mine was telling me about a storm that knocked down a power line over at their place, and it got me to thinking.  Why are downed power lines dangerous?  I don't see any good reason for it.
It seems to me that if they can put a GFI on a hair dryer that will kill power within a fraction of a second if it falls into the sink or tub and shorts out, they ought to be able to do the same thing to a power line.  Is there any reason why the basic concept can't work at that scale?  Or if not, why aren't they standard equipment on power lines?
 A: Even if you could cheaply and efficenctly engineer a GFI to work on 250,000V high current lines, and you could shut down the grid to fit them how often do downed lines hurt people compared to lawn mowers going over extention leads?
Even then I suspect that if you could disconnect the other end of the line there would be enough charge stored in the cable between you and the GFI to make you very unhappy
A: Downed power lines are dangerous because they may still be live. 
A downed power line (or any other ground fault) can be deadly even if you do not touch the line itself, due to the phenomenon of step-potential and earth-potential rise. Check this Wikipedia reference for more info on step-potential:
http://en.wikipedia.org/wiki/Earth_potential_rise#Step.2C_touch.2C_and_mesh_Voltage
To answer your second question: Power grids do use electrical protection systems to stop the flow of current in event of a fault. However, for an LV line (110Vac in America, ~240Vac most other places) you may find the nearest upstream protection device is just a fuse. For MV lines (1000Vac+) the protection is likely to be a device called an auto-recloser or sectionaliser, which are more sophisticated than fuses but still cannot be relied on to make a downed line safe.
An example of why a downed line might remain live is if distributed generation (e.g. solar panels or a local wind turbine) have been connected to the grid downstream from the nearest protection device. The distributed generation could potentially continue to feed the downed line even after the protection system has operated. (If the DG has been well designed and implemented it should have its own protection system to prevent this, but it remains a possibility.)
A: The entire network can still receive lightning from storms, however distant, and deliver them in your body. If you think you can turn off the storm then it will not be dangerous. 
