In 1971, astronaut David Scott conducted Galileo's famous hammer/feather drop experiment on the moon, during the Apollo 15 mission. Galileo had concluded that all objects, regardless of mass, fall at the same speed -- however, the resistance caused by the air (as in the case of the feather in Earth's atmosphere) can cause the feather to drop slower. Well, on the moon there is no atmosphere (a vacuum), so the objects should drop at the same speed. See for yourself how the experiment turned out in the video below.
As Mission Controller Joe Allen wrote in the Apollo 15 Preliminary Science Report:
During the final minutes of the third extravehicular activity, a short demonstration experiment was conducted. A heavy object (a 1.32-kg aluminum geological hammer) and a light object (a 0.03-kg falcon feather) were released simultaneously from approximately the same height (approximately 1.6 m) and were allowed to fall to the surface. Within the accuracy of the simultaneous release, the objects were observed to undergo the same acceleration and strike the lunar surface simultaneously, which was a result predicted by well-established theory, but a result nonetheless reassuring considering both the number of viewers that witnessed the experiment and the fact that the homeward journey was based critically on the validity of the particular theory being tested. Joe Allen, NASA SP-289, Apollo 15 Preliminary Science Report, Summary of Scientific Results, p. 2-11
Here's video of the experiment:
Ever since the hammer/feather drop in 1971, moon-hoax conspiracy theorists have been trying to prove that this footage was faked. Here's one video that claims to disprove NASA's experiment. I encourage you to read the YouTube comments on that hoax video for an entertaining nerd-fight. See also: high-resolution video of the experiment from NASA, and a mathematical discussion of the physics involved.