In order to answer this question, we need to understand something about the resolving power of telescopes. Take a look at this image. This is an aerial image of the statue of liberty made available by a Web site called TerraServer. This image has 1-meter resolution, which means that something on the ground that is 1 meter square produces one pixel in the image. In the image of the Statue of Liberty, her head is about 3 meters across, so her head should take up about 3 pixels by 3 pixels in the image (see this page for other fun Statue of Liberty facts).

So, a good spy satellite might have 1-meter resolution like this. The best telescope available today is the Hubble Space Telescope. It has a resolving power of 0.1 arc-seconds. I am open to correction on this, but as best I can tell, the Hubble telescope would have something like 15-centimeter resolving power if it were pointed at something on the Earth, like the Statue of Liberty (if you are a telescope expert, please write in and correct me if I am wrong). Fifteen centimeters is about half a foot.

The moon is about 1,000 times farther away from the Hubble Space Telescope than the Earth is. That means that if you pointed the Hubble at the moon, it would have 150-meter resolution. At that resolution, a football stadium occupies just one or two pixels of the image. That means that there would be no way to discern the Lunar Excursion Module or any of the other equipment left on the moon. It is just too small to pick up, even with the world's best telescope.

 Evidence? Several alert readers pointed out that, even though you cannot see direct evidence of the moon excursions with a telescope, there is one artifact that the astronauts left behind on the moon that does provide evidence of their missions. That artifact is a laser beam reflector that has been used to track the distance of the moon from the Earth. This article talks briefly about the reflector. A true skeptic could argue that this reflector was placed there by a robotic satellite, or that it is a piece of convenient obsidian found randomly on the lunar surface...