Wikia

Azeroth has two moons:

The larger, bright and silver moon is known as the White Lady. The night elves know and worship it as Elune while the tauren refer to it as Mu'sha (the left eye of the Earthmother) in Sorrow of the Earthmother.
The smaller cool, blue-green moon is known as the Blue Child. The "Blue Child" is currently not visible in WoW, though it once was. It was removed from the game at the release of The Burning Crusade, possibly due to a graphical error, it will be added back in Mists of Pandaria.
The Earthmother sent the Blue Child away to learn about the universe upon noticing the coming of the Burning Legion, explaining its disappearance prior to the Burning Crusade expansion. It will be a very long time before it returns.

Just before Loken in Halls of Lightning there is a globe/projection of Azeroth with its two moons in orbit around it.

The White Lady is usually fully visible at around 22:30 server time.

Sources

The larger of the two moons had risen first this evening, and now hung pregnant and silver-white against a clear, star-dappled sky.

The quest Of Love and Family refers to the twin moons of Azeroth.
Lord of the Clans also makes several references to two moons.
How to Win Friends also makes reference to the moons.
A conversation with a GM revealed that lore-wise, the Blue Moon was removed as it was sent to explore and study the rest of the universe although its removal due to skybox graphical errors was never denied.

In the Warhammer universe, there are also two moons: Mannsleib, which is like Earth's moon, and Morrslieb, a green (however not blue-green), smaller and magical moon.
Multiple moons are a common element of many fantasy and science fiction settings.
In the Mists of Pandaria beta, the blue child has returned to the night sky. It it yet unknown if this means the moon will return for Patch 5.x.