Minecraft wiki entry for Sugar_Cane, associated text: When a sugar cane is broken at the second level, the time resets (for example, if a two-block high sugar cane is broken, but is just about to grow to the third stage, it would reset that time).
By placing more sugar canes on top of a sugar cane plant, it is possible to create tall sugar canes (up to y=255, the maximum height for building), although they do not naturally grow this high.
Before sugar cane received an official name, they were sometimes referred to as bamboo, a block added 9 years later. Other names were "reeds" and "papyrus".