The Secret Lunar Base
Our moon factors heavily into a few different space conspiracy theories. One such theory is that not only have we been to the moon, but someone has built a fully functional lunar base on the far side.
The moon is in tidal lock with the Earth. That means the rotation of the moon has slowed down over millions of years to the point where the same side of the moon always faces our planet. It's called tidal locking, and it means that whenever you look up at the moon you'll always see the same features. It also means the far side of the moon -- sometimes mistakenly called the dark side -- is out of view.
You have to admit, a base located on the far side would be safe from prying eyes. But who could have built such a thing? The theories postulate everything from the Nazis in World War II to the United States to aliens. We've certainly had a look at the far side of the moon a few times -- many of the Apollo missions passed the other side and took amazing photographs. But images and video from these passes show no signs of secret moon bases.
It doesn't help the conspiracy theorists that some of the evidence they've pointed to in the past turned out to be promotional efforts for movies like "Iron Sky" or "Transformers: Dark of the Moon." So far, it appears that science fiction is the only place you're likely to find a lunar base.