Here's what I think would be some reasonable guidelines for the number of EM programs one should apply to:
Pluses:
A strong interest in EM
(Obviously if you don?t have this, you?ll have problems no matter how good everything else is)
Strong clinical grades
Strong board scores
AOA
Strong recommendations from EM residency faculty
Strong EM clerkship grades (best if done at the program(s) you want)
Published or presented research (the university-based programs tend to favor it).
Minuses:
Failed boards
Failed a rotation
If you have ALL pluses, you're pretty exceptional, and can probably apply to a minimum number of residencies (say as few as 5-10), in order to get enough interviews and still match.
If you have at least two of the above 5 pluses, with no minuses, you can probably count on a sufficient number of interviews by applying to 10-30 programs, depending of course on how selective they are.
If you are somewhere in the middle (one or two of the pluses with or without any minuses), you will probably need to cast your net a little wider than 30 programs, say 30-50.
If you have minuses, and don?t have many (if any) of the above pluses, you will want to at least consider applying to close to all 124 programs out there, concentrating on the less selective ones. You will obviously spend some money doing this.
Keep in mind that this is only from the perspective of trying to obtain interviews. Once you get an interview, the playing field is more level between you and the other applicants. While many residency program directors would like to have someone with strong academics and clinical acumen, they probably don?t want to have to deal with a prospective resident who will be high maintenance, who doesn?t get along well with others, or who will just be a pain to deal with, no matter how good they are on paper.
Note: I did not include factors such as being a DO student or FMG, as I would be interested in what those who have gone this route (e.g. Quinn, Apolyon) would have to say about it. The above points are only my own thoughts, and I would welcome any input from others.