Earth's Moon, also known as simply the Moon, is the only moon that orbits the planet Earth. It was subject of many exploratory missions of the Tau'ri during the middle part of the 20th Century. These missions, however, were largely abandoned during the 1970s.
The first manned Moon landing occurred in July of 1969. Lt. George S. Hammond watched it in a hospital room at the bedside table of his father, who had his first heart attack just two days earlier. A few weeks after this, SG-1, having been sent back in time through an accident with the Stargate in 1999, used this information to prove to Hammond that they knew him in the future. (SG1: "1969")
In 1997, David Swift, the United States Secretary of Defense, compared the status of the Stargate Program to that of the Apollo program, stating the Apollo program had been discontinued because the astronauts brought back items of little value, like Moon rocks. (SG1: "The Nox")
When The Trust stole the Stargate Command's Stargate in 2004, bringing it aboard Osiris' cloaked Al'kesh, they put the ship in an orbit around the Moon. While they were orbiting the Moon, Earth's "point of origin" symbol could still be used to create a valid gate connection. Presumably this means that if the Moon had a gate it would be reached with the same gate coordinates as Earth. (SG1: "Endgame")
After the Extraction Ceremony conducted on the last Ba'al clone, Colonel Samantha Carter talked with Major General Jack O'Neill about the new moon base. It is however unknown if she meant Earths moon or another. (SG1: "Continuum")