Sugar is a rather broad term, I'm assuming you mean white refined sugar (sucrose, a disaccharide).

You absolutely don't need to to eat any sugar at all. Simply put, glucose (a monosaccharide) is what normally power our cells. Glucose can be produced from hydrolyzing longer carbohydrates, or even from fat and proteins via gluconeogenesis.

Suggested reading:

http://en.wikipedia.org/wiki/Gluconeogenesis

http://en.wikipedia.org/wiki/Citric_acid_cycle

http://en.wikipedia.org/wiki/Sugar