I've been to the Great Wall of China four times now - three times to the Mutianyu section and once to Badaling. I've never seen more than a few people at the wall on any of the visits, and definitely nothing resembling the huge crowds that you see in photos sometimes.
The secret? Either head there in the off-season, or go in the late afternoon. In this case we got to the Mutianyu section on a weekday in May around 2pm. We stayed until the cable car down was about to close - roughly 5pm. We passed a few people, but most of the time we didn't see anyone else.
Other than the timing, the smartest thing that we did? We bought a Chinese robe and two umbrellas at the base of the wall for my cousin's wife. With no one on the wall, the photos wouldn't have been interesting otherwise.