The Organization was brought in for several reasons.
One, as everyone has already mentioned, they were brought in to be the antagonists of not KH2, but also KH: CoM. Once the main villains that inhabited KH1 were destroyed, there was obviously need for others to take their place. Insert Organization.
Two, the Organization gives KH more originality. Now, instead of the villains just being Disney characters, with the exception of Ansem, SoD, we have more original characters, which makes KH seem less like a hodgepodge of different ideas and stories.
Three, it brings a certain more depth to the story that wasn't there before. Obviously, most people don't consider the entire Organization to be wholly evil, like Sora does. Even Naminé, who was kidnapped by some members of said Organization, straddles the fence where the true evillness of Organization XIII is concerned. When you think about it, all of the memebers of the Organization used to be somebody. They lost their hearts through some way (including the Original Six, who were only doing this in the name of science- except for Xehanort) and were once people with feelings, ideas, thoughts, and loves. Plus, the heart breaking (at least for most females) story of the friendship between Axel and Roxas adds a depth not originally there. So, plot-wise, it was a great addition.
Fourth, they're all really great looking, and would draw in more sales. I've even heard of some people that only bought the game to begin with just because of the way the Organization members looked- even without their hoods off.
