I've gotten a ton of requests over PM and I can't really keep up anymore. Here is the basic, unedited gist of what I have been telling people. This has been my approach, so take it for what it's worth.
Also, look at this thread where this was discussed (by me and others) previously:
http://forums.studentdoctor.net/showthread.php?t=347225
I, like everyone else, am just kind of guessing about this stuff. But I think they're a good guesses informed by discussions with current med students, current adcom people, and my own experiences. Plus I do hiring in the medical field, and I also have worked for admissions at my undergrad institution. I have a fairly good sense of how these people think.
Personally, my application looks pretty chincy on paper; I really think my strength and good fortune in this process has been my writing background and putting a lot of energy into all my essays and letters.
As I mentioned, I've been accepted to a few good schools with stats below their averages and ugly things on my transcript (a 2.7 GPA my senior year, many withdrawls, etc.). My MCAT was ok, but not high enough to make up for my GPA. (And I'm white and privileged, in case you're wondering.) I really think my letters made a difference there. One of the reasons I think that is because I got a response from one school in particular a little later than all the other people who interviewed my week, which makes me think that they took my letter and update and made sure that my reviewers had it in hand before bringing my file to committee. (That's pure conjecture.)
In terms of your letter, try to make it as specific as possible -- not only to the school, but to the addressee. Is there someone you met and had a particularly good conversation with during your time there? And is he/she on the admissions committee? I would address it to that person. If you don't have any connection to an adcom person, I would address it to whoever would allow you to make the letter the most personal and cc the dean or adcom people. In your letter, try to make them remember who you are, but don't be too cheesy (don't say, "remember how we talked about your pet squirrel?") Just drop something subtle about your work, or your undergrad, or something you talked about that is related to the letter at hand. Something that'll help them place you. But make sure it's integrated into the content of the letter.
One thing you might want to add is somehow get in there that you've been interviewing at a lot of great schools (if that applies), but you like them the best. Don't be as forceful as that, but do say something to the effect of "while i have had the opportunity to visit a number of excellent medical programs, i find your program stands out in this way ..." Don't be specific about the schools you're comparing, and don't be negative about the other schools. Just make it clear why that school is more ideal for YOU than those other schools.
In terms of a format, I think starting out with an update is a good way to go because it legitimizes your reason for writing. If it's just a letter that says "yoohoo, I'm still here, don't forget about me," it'll seem wimpy and unecessary. Of course that is your real purpose, but at certain schools especially, they might not be as charmed by that kind of thing. Update could be anything from offering new grades, discussing future plans, or simply saying, essentially, "I'm this far along in my application process, it's been X months since we've last been in contact, and I still consider your program to be my top choice ..."
After the update, you could get to part B and basically say "Further, as the admissions committee considers my application, I would like to express my continued, very strong interest in attending ___ medical school." (That language only works if you're writing to an adcom member, but you get the idea.) Then launch into your reasons, and try to include the addressee in the conversation. I don't think it really matters what you say here, but make sure it's personal. Don't just say it's a great program with great opportunities. They already know that. You don't need to list all their strengths for them. You need to let them know why it's the perfect program for YOU.
Also, in my own experience, I've interviewed at a lot of schools recently, and I really leave each and every one with a good sense of the "type" of student they want at their school. And it's different at every single school. Be sure to cater to that "type" and highlight how you not only match that "type," but also that you share the feeling that these are important qualities for the student body. This also must be very subtle. But try to show basically that you and the adcom think alike. You are obviously qualified enough to be accepted at this school -- you just need to make sure they know that you fit well into their image of an ideal ___(your med school)___ student.
Again, this is my own approach, and it's definitely not the only way to go. I'm a writer and editor at heart, so if anyone wants to send me drafts, I'd be happy to take a look. Good luck to everyone!