Prag has proclaimed the correct spelling to be Taijituan, and as Prag has been here since the dawn of time and tends to be right on that sort of thing, I've sort of adopted it as the 'right' one. Personally, I like Taiji because it's a little friendlier and nice-sounding. Okay, okay, and it's shorter to type. Shoot me, I'm a little lazy that way.