According to the National Weather Service, a tornado is a "violently rotating column of air extending from the base of a thunderstorm down to the ground." They are rated using the Enhanced Fujita Scale
Tornadoes have occurred in all 50 states. Texas, Louisiana, Mississippi, Alabama and Florida are all tornado prone.
As far as strength is concerned, tornadoes are rated using the Enhanced Fujita Scale.
EF-4 and EF-5 tornadoes are classified as "violent." Although rare, most tornado-related deaths are a result of violent tornadoes.