http://hubblesite.org/reference_desk/faq/answer.php.cat=topten&id=77

Can Hubble see the Apollo landing sites on the Moon?

No, Hubble cannot take photos of the Apollo landing sites.

An object on the Moon 4 meters (4.37 yards) across, viewed from HST, would be about 0.002 arcsec in size. The highest resolution instrument currently on HST is the Advanced Camera for Surveys at 0.03 arcsec. So anything we left on the Moon cannot be resolved in any HST image. It would just appear as a dot.

The laser reflectors alone prove we went there.

As others have noted, the Hubble isn't designed for that. If you've ever pointed a backyard telescope at the moon, you know how significantly brighter than anything else in the night sky, the moon is. No point in fucking with the Hubble's extremely sensitive light-detection equipment just to debunk idiotic conspiracy theories.

Anyway, a few years ago the Lunar Reconnaissance Orbiter mission took hi-def photos of several landing sites.

http://www.nasa.gov/mission_pages/LRO/news/lro-briefing-20110906.html#.V3l1kzX52MU

https://www.nasa.gov/mission_pages/apollo/revisited/

Here's Apollo 17: You can see the descent stage as well as the ALSEP equipment left by the astronauts and the lunar rover tracks-



Here's Apollo 11 for comparison. As you can see, they didn't really migrate all that far from the LM, and understandably so. The mission was mostly about landing and getting back in one piece.

Not with any remarkable detail, but enough to make out the landing sites and the Rover tracks leading to and from them.

Not to mention the flag that got knocked over when they lifted off.

The paths left by astronauts Alan Shepard and Edgar Mitchell on both Apollo 14 moon walks are visible in this image. (At the end of the second moon walk, Shepard famously hit two golf balls.) The descent stage of the lunar module Antares is also visible.