What organization is this referring to?

actually its the Roman Catholic Church.

Some have said it is the Catholic Church and others Rome for Revelation 17:18 says, "The woman you saw is the great city that rules over the kings of the earth." And Rev. 17:9 says, "This calls for a mind with wisdom. The seven heads are seven hills on which the woman sits." Rome is the most likely reference but Mecca also has seven surrounding hills.

Godspeed.

The Roman Catholic Church

It sounds like you have already guessed who she is. This video explains who she is in Biblical detail. It is about an hour long and it is very informative...based on David Hunt's book "A Woman Rides the Beast"

http://www.youtube.com/watch?v=w5Ke7Tn3uOU

Any religious organization that places itself between its followers and God.

In particular, it applies to hierarchical religious organizations like the Watchtower publishing corporation (Jehovah's Witnesses).

Revelation says to "get out of her."

“And he [the angel who appeared to John] carried me away in the power of the spirit into a wilderness. And I caught sight of a woman sitting upon a scarlet-colored wild beast that was full of blasphemous names and that had seven heads and ten horns. And the woman was arrayed in purple and scarlet, and was adorned with gold and precious stone and pearls and had in her hand a golden cup that was full of disgusting things and the unclean things of her fornication. And upon her forehead was written a name, a mystery: ‘Babylon the Great, the mother of the harlots and of the disgusting things of the earth.’ And I saw that the woman was drunk with the blood of the holy ones and with the blood of the witnesses of Jesus. Well, on catching sight of her I wondered with great wonderment [but, of course, not admiringly].”—Rev. 17:3-6.

The fact that the woman was “drunk with the blood of [God’s] holy ones and with the blood of the witnesses of Jesus,” what does that prove? It proves she is against Jehovah God and against his Son Jesus the Messiah or Christ. She is therefore not on the side of the one true worship, the one true religion. The name on her forehead, although a mystery, betrays who the woman is. The main part of her name is the name of Jehovah God’s ancient enemy, Babylon. But she is greater than that city built under Nimrod’s direction on the Euphrates River; that is why she is called “Babylon the Great.” The ancient city of Babylon was, clear down to its disastrous fall in 539 B.C., outstandingly religious; she was a leader in false worship. Ah, now, we see that the mysterious Babylon the Great is, not pagan Rome of the seven hills, but the world empire of Babylonish religion that gathers all the world in under its dominion.

That is why the angel said to John in explaining the mystery: “The waters that you saw, where the harlot is sitting, mean peoples and crowds and nations and tongues. And the woman whom you saw means the great city that has a kingdom over the kings of the earth.” (Rev. 17:15, 18) She sat on those symbolic waters and held kingdom over earth’s rulers long before the scarlet beast was set up as an idolatrous image. As soon as this symbolic wild beast appeared after World War I she climbed on its back. In view of her religious power, that was easy for her. When the scarlet “wild beast” went into the abyss during World War II she continued to sit “on many waters,” namely, on the peoples, crowds, nations and tongues, and to exercise “kingdom over the kings of the earth.” (Rev. 17:1) When the “wild beast” ascended out of the abyss with the help of especially its seventh head, the Anglo-American World Power, Babylon the Great at once climbed upon its back, and there she sits till this day.

It was but to be expected that she would ride this beast, it being a political organization, a world power. Babylon the Great is a harlot and is named “the mother of the harlots.” God’s angel said she is the “great harlot who sits on many waters, with whom the kings of the earth committed fornication, whereas those who inhabit the earth were made drunk with the wine of her fornication.” (Rev. 17:1, 2) Since the scarlet wild beast symbolizes a political organization, the Eighth World Power, and its seven heads symbolize “seven kings” or seven world powers, Babylon the Great would follow her regular course and commit fornication with it just as she had committed fornication with the previous seven world powers and other “kings of the earth.” Symbolically speaking, she would be committing fornication with a wild beast, which act is bestiality, a sin that is loathsome and that is condemned by God’s law.—Lev. 20:15, 16.

What makes you think it is an organization? Personal bias? Typically, Babylon referred to the Roman Empire (or it referred to the actual city of Babylon).

Catholic Church, read the link it shows you who it's talking about

The Church of the devil.

Catholicism.