About that nose...

Among many of the mysterious aspects of the Great Sphinx (to specify, since there are a number of sphinxes throughout Egypt) is its conspicuously missing nose. One might wonder if its popularity would be what it is today if not for its interesting and obvious "deformity."

And, of course, EVERYONE knows how it happened, right?

They certainly think they do.

There's a great many versions of who and even whys. The thread of military destruction is common and useful when proving certain "points" about the military and its mindset (as well as propaganda to make the other country's army look bad). Some Afrocentrists even claim it was done for racist reasons because the Sphinx had black features:
White folk try to rewrite history and write us out. White supremacy caused Napoleon to blow the nose off of the Sphinx because it reminded you too much of the Black man's majesty.
Louis Farrakhan addressing the Million Man March
Another person who knows.

Some background about the monument
The Great Sphinx was carved from soft limestone (this will be important later). Some think it began as an outcrop that vaguely resembled the finished product, inspiring the creators to make it. The length is 60 m (200 feet) and the height 20 m (65 feet). Its face is 4 m (13 feet) wide with 2 m (6 feet) high eyes. In addition to the nose, the ritual beard (on display, in fragments, at the British Museum) is missing and part of the uraeus—the sacred cobra headpiece—is gone.

In general, the whole thing is crumbling due to wind, humidity, and smog (from Cairo). There have been numerous attempts to reconstruct or preserve it and some have even made things worse. It has been covered by sand many times over its lifespan, the first record going back to 1400 BC. There have been at least four "clearings" since 1800.

Whodunit?
The checklist can be pared down rather quickly, actually. It's well known (there are pictures and photographs, plus firsthand accounts) that the nose was definitely absent prior to the 20th century (goodbye Nazis and probably the British, too).

In fact, the British can be summarily dismissed from the picture. No contemporary account prior to Napoleon's arrival describes it with a nose. Since that wipes out the 1798 version, the 19th century one falls as well.

There was a picture drawn by a British traveler who visited the site in 1737 that showed the Sphinx with nose intact. It is likely that he "added" the nose and it was already missing. This wouldn't be the first time: in 1579, a Johannes Helferich drew a copy with nose and with very feminine features (a rather poor cartoonish drawing, the most notable female feature being breasts). On the other hand, King Christian VI (Denmark) sent an expedition to the Nile area in 1755. Among the members of the expedition was an artist who drew detailed pictures of many things—including a noseless Sphinx. It is very doubtful that someone would draw a noseless Sphinx when it really had one. That dates it at 1755, at least. It had to have been lost earlier.

Now, as to the Arab possibilities. Both are mentioned in contemporary accounts saying that violence was done to the Sphinx. This might be true, though it's difficult to determine the veracity of the accounts. In particular, the story of the Islamic cleric Sa'im al-dahr. While it does mention damage to the nose, it also mentions damage to the ears, something that clearly isn't the case.

Another explanation
Egyptain monuments are ancient and have stood the test and ravages of time for thousands of years. Part of the reason, aside from climate, is that many of them are built of sturdy material: granite. As noted above, not so in the case of the Sphinx. It's not quite clear just how much damage the monument has sustained over time. But it is crumbling. It is the subject of restoration work. And was in the past.

It's rather difficult to see how such a large unsupported appendage (soft limestone, remember) would not have suffered a great deal of weathering over the years, up to and including, the distinct possibility of its having fallen off in bits and pieces or larger chunks or simply worn away. In fact, some archaeologists believe that the reason it is in as good a shape as it is today, is that it has been periodically covered by sand, protecting it from the weathering elements.

This would suggest that even if one or both of the Arab accounts is true, the extent of the damage cannot be determined since time and weather had already been at work for a few thousand years. And continue to this day.

(Sources: http://home.xnet~warinner/sphinx.html, www.catchpenny.org/nose.html, www.nmia.com/~sphinx/egyptian_sphinx.html, www.touregypt.net/sphinx.htm)