The Sphinx, as ancient as it is, was in relatively good condition until it was vandalized by the Muslims.
Thanks BenLurkin, Talisker, Joe 6-pack, rellimpank, Daffynition, Campion, TASMANIANRED, anyone else I’ve missed.
The two main stories I’ve seen about the nose are, Napoleon’s troops, and the Turks (both using it for target practice).
The fact is, alas, that no one knows when the nose went missing. AFAIK, the only image of the Sphinx in profile that survives is the twofold on on the Dream Stele, which dates from the 18th Dynasty, during the New Kingdom.
Breaking off the noses was a superstitious practice that was intended to “kill” the spirit of the thing. The name Sphinx is a corruption of an pharaonic Egyptian term which translates as “living image” (something like “shesep kaf”).
Given the usual state of the Great Sphinx — buried up to the neck in sand — and the quality of the bedrock, it’s pretty likely that the nose came off on its own and got carted off for construction, and it probably must have happened after the 18th Dynasty.
I’m inclined to agree with Talisker, that the Sphinx was originally a representation of Anubis, and (again, because the body’s usually been buried; Herodotus didn’t even mention the Sphinx) the stone crumbled away, which led to the stump’s being resculpted. The face could have been carved during the Nubian Dynasty, which fits very well with the physical traits others have found through analysis. That dynasty also portrayed pharaohs as sphinxes.