Going off of what BeardedRunner said, here are my opinions from what I have gathered from my experience (applying to med school 3 times) in the last few years:
-Shadowing is great; it gets you exposure to clinical medicine that is difficult to get any other way (except SOME volunteering). Don't do too much with one type of doc bc it's going to be pretty repetitive and adcom members have told me it is a very "passive" activity; you may get lucky and work with a really cool and engaging doc that lets you do a good amount, but that is somewhat unlikely. I would recommend moving among a few fields to show that you have seen what they do and still actually like it. Don't spend more than 20hrs or so with any doc.
-If you are interested in research (or going to a very research oriented school), this is a necessity. I did VERY little (practically none) bc I have absolutely no interest in any sort of research in the future. Adcoms will be able to tell if you were really interested in it, or just doing it to put on your app.
-IMO, going to a 3rd world country is as close to a guarantee to getting in as anything else after GPA and MCAT. Whether or not you agree with the underlying reason for going on the trip, doing something abroad shows you are interested in helping the "human race." Plus, the trips I have been on have been incredible and very eye-opening. Check out Global Medical Training (gmtonline.org). I did a trip with them and have quite a few friends that have done trips with them. THey are great and very accomodating.
-In terms of volunteering, do something you will enjoy, whether it is at the YMCA, Soup Kitchen, Homeless shelter, hospital, clinic, etc. I think adcoms would rather see you VERY involved with 1-3 volunteering opportunities than slightly involved in 10. I found my niche at a free clinic in my hometown and in the oncology unit of a hospital. Bottom line: doesn't have to be medically related if you have other medical experience (trip abroad and shadowing).
-Leadership roles are definitely important, but probably lower on the list of things to have. I would get the above before leadership. I had a few leadership positions, but I don't think they helped me TOO much (definitely didn't hurt).
-I agree with the EMT thing. IMO, good volunteering and significant clinical experience (research, volunteering, shadowing) will be more beneficial than an EMT. Obviously, some people disagree.
Sorry for the novel. Hope this helps....