If you want to know how I got into Yale, I would say it was probably because of my essays-- specifically my 250. I took the essays very seriously, I took the 250 very seriously, and I think that might have made me stand out. My 250 was argumentative and on a philosophical subject. Also, my essays were complexly punctuated. Who knows, maybe the Profs. at Yale appreciated my appropriate usage of colons, semicolons, commas and em-dashes.
My letters of recommendation were very strong, so that probably helped as well. Why not Harvard and Stanford? Well, they didn't get to read my 250. Also, I think admissions committees might not be as willing to take a chance on someone like me as Profs. would be. Perhaps that was why I had greater success with Yale, where the Profs. do the choosing.
Really though, I have no idea why I got in. I'm just pretty thrilled about it. My advice to future applicants is to take your essays very seriously. Why are you awesome? Why should they choose you over others with similar or better numbers? The essays are your chance to let them know! Another piece of advice: if you are thinking about applying to Yale, but your numbers are a little bit on the low side (like mine were), apply anyways! Anything is possible. If you don't apply (or if you put in a half-hearted effort on the 250) you might always wonder what would have happened had you tried harder.
Finally, the best piece of advice I can give is not to spend the time after you apply obsessing! It will accomplish nothing other than making you miserable. I was miserable from November right up until when I heard from Yale, and it was truly a waste of months of my life.
GOOD LUCK!!
You've given me a lot of hope. :) I'm almost afraid to *want* Yale because it's such an admissions black box, but seeing as you got in with relatively low (for Yale) numbers has inspired me to just go for it. Congrats and thanks!