One of the reasons I like this show is its great characters. Let's get started with the typing.
Brennan: EST? - I was about to type her as an introvert because she lives a bit like a loner, but thee way she says what she's thinking all thee time, and how she seems so comfortable in social situations despite her social awkwardness, makes me think she's an extrovert. I'm pretty sure she's a sensor because of her attention to detail and how she is very concrete in her thinking. The T is probably the most obvious. The last one is a bit of a guess because I'm having a hard time remembering examples that point to either J or P.
Booth: ENFP - He's an extrovert for sure. He's a social guy. I'm typing him as an intuitive mostly because of the way he makes intuitive leaps, and the way he makes up "stories" about how he thinks the murder happened. It's a little hard to tell if he's an F or a T because he's on the job for much of the show, but if you look at his life I see more of an F leaning. And then P because of the way he continues searching for things instead of making up his mind completely.
Zack: I?TP (with Aspergers)
Those are my guesses. Your turn.