To me, this is a question of form versus function, and function should come out on top here. Sure, it helps if your personality naturally fits with the school, but the majority of your effort should be spent making sure that you highlight your qualifications. No school is going to want to turn someone with superior qualifications away just because their essays don't show the right personality (well, maybe if you sound like a serial killer...). You can get a sense of what they are looking for by looking at the essays.
Personality types by school (in my opinion):
HBS: Your personality should be that you are better than everyone else (and in fewer words!). Wait, is that a personality trait? Seriously, I find HBS completely cold and unfriendly.
Stanford: Quirky and confident; self-aware. Positive attitude. Willing to explore new things and break free of the status quo.
Wharton: I think most people would describe Wharton grads as cold and efficient, but I actually think the school is looking for a little heart in its applicants. The essays seemed very accomodative to me.
Chicago: From what I have seen, the stereotypes are true -- anti-social and geeky quant types. They do not seem willing to work with people who deviate far from the path. Rhyme, you want to chime in?
Columbia: Your personality is that you love Columbia, only Columbia, and are not planning to use the school as a backup (dang it, how did they know?)
Kellogg: Did not apply. Seems like they want people who are collaborative and a little campy. Don't be a jerk.
MIT: Did not apply.
I didn't look at anything outside the M7, but you can probably get anything you need off of the school's website. Most of the stereotypes you will hear are based on something, so that might be a good place to start -- figure out what the buzz is and then adjust it a little to fit your own situation and profile.