Let me see if I can get this straight: there's Kingdom Hearts which is the end all be all, the alpha and omega, the place where all life in the universe is born and where it all goes to die, which Ansem tried to get to in KH1 and poked it's head out of the Realm Of Darkness when it sensed the Imperfect X-Blade being forged. Then there's Xemnas's artificial Kingdom Hearts that was created from amassing the freed Hearts of the Heartless. But in some places I've read that the one Ansem was after and the one that Master Xehanort summoned were not the actual Kingdom Hearts and were also facsimiles. My question is how many Kingdom Heartses are there and which ones are real?

Every single KH we have seen so far has not been the real one. There all fakes. Yes very powerful fakes but nothing like the real one. What is the real one? we've yet to know

There is a Kingdom Hearts of people's hearts and a Kingdom Hearts of worlds' hearts. They aren't the true ones though as the true Kingdom Hearts lies in darkness.

If the one that Ansem was after was the Kingdom Hearts Of World's Hearts and Xemnas's was the one Of People's Hearts then what about the one that showed up at the Keyblade Graveyard? This really should have been explained in the games. *shakes fist at the Japan exclusive guide books and interviews*

Well, it seems that Xehanort's multiple attempts at gaining Kingdom Hearts have ended up in fakes that, while powerful, aren't quite powerful enough!  But now that he has his plan all panned out, this time, he'll get the X-Blade, and perhaps the true Kingdom Hearts shall emerge from the darkness in response to the X-Blade's reconstruction, ya know?

Although, if one of the Norts did get their hands on one of the non-True Kingdom Heartses it still would have gone a long way to help get the real deal, phenomenal cosmic power and all that. Which I guess explains why none of them are too bummed about not getting them, they were just added bonuses on top of The Master Plan.