A 16th century Arab historian, Al-Maqrizi, attributes the loss of the nose to a Sufi Muslim named Muhammad Sa'im al-Dahr in the 14th century. Upon finding the locals making offerings to the Sphinx in the hopes of having a good harvest, Sa'im al-Dahr became so outraged, that he destroyed the nose. The locals, who were hoping for a good harvest, realizing that a damaged Sphinx might be pissed off enough to make things worse, became so pissed off themselves that they hung Sa'im al-Dahr.
Other accounts state that a cannonball fired by Napoleon's army (or possibly the British army) took out the nose, but sketches made previous to Napoleon's Egyptian campaign show the Sphinx without a nose.
1738 sketch by Fredric Louis Norden. Napoleon was born in 1769.