Tornadoes used to be classified according to the Fujita Scale. Developed by Ted Fujita and his wife in 1971, the scale has been a famous general marker for how intense a tornado can be. Recently, the Enhanced Fujita scale was developed in order to further classify a storm based on damages.
Famous Tornadoes
There are many different tornadoes that have been infamous in the lives of those most affected by the storms. Several have had notoriety for other reasons. While not named like hurricanes, tornadoes will often get a colloquial name based on their location or damage patterns. Here are just a few:

