I did things a little non-traditionally, but apparently it all worked out in the end.
First off, you will want a letter from your Dept Chair. They will expect this and generally set aside time each year (around July/August) to meet with aspiring anesthesiologists. All I had to do was e-mail his secretary and they took it from there (gave me a time, told me what to bring - grades, PS, transcript).
So this leaves you with two more letters in most programs. I got my second one from my advisor (who turned out to be the PD at my school). He was well-known in the field and wrote a nice letter. I didn't do any work with him at all, and only met with him about 3 times prior to his writing the letter. I really wish I could have had a letter from someone I worked closely with, but I actually had a truly awful attending when I did my 3rd year rotation in anesthesia and wouldn't ask him for cold **** on a plate if I were starving, much less a letter of rec.
For my third letter I went to the Chair of the Dept of Medicine. At my school, this individual writes over 100 letters each year and gives the distinct advantage of ranking students relative to each other (which our school does not do). This really helped me as I didn't get AOA but he actually wrote in the letter that he didn't understand why I wasn't AOA. I believe this letter helped me for that reason, and because this guy writes so many letters that all the programs I applied to were very familiar with him and what he wrote.
From the vast majority of people I've talked to, you'll want to get (in addition to your Chair's letter) something from an attending you've worked closely with during a rotation (preferably anesthesia, but not necessarily). This is something I wish I would have been able to get. My best friend (who is also doing anesthesia) actually got one from his OB/Gyn attending who knew him very well. He told me he got great compliments on that letter during interviews.
I'm sure some of the attendings and residents out there may have a different take on this, but that's the advice I would give people regarding LORs.