I think becoming an EMT and USING your skills by either volunteering or working is a great asset to your application. The reason I put "using" in caps is because there are a surprising number of people who get certified just to put it on their application, but they gain no experience in the field. If you plan on doing this, I wouldn't bother wasting your time or money.
However, even if you become an EMT-B (the lowest level on the EMT scale) you have a great opportunity to begin assessing patients and gaining great communicational skills which will all be vital to becoming a doctor. EMT's are usually the first on scene, which provides a great way to begin assessing situations. You will get a lot of direct patient contact, as well as take vitals, intubate, and use different medical devices (e.g. glucometer). Take note, however, that there are different levels of EMT's and the skill capacity differs amongst levels. Sure, there are other jobs such as phlebotomy that will allow for direct patient contact. Realize however, that (depending on the level of EMT) EMT's are able to start IV's just like phlebotomists, but are also able to so much more.
Anyways, I am by no means bashing on any other jobs...I'm just trying to prove that this opportunity has incredible potential to look great on any med school application if it is taken seriously.
Also, I wanted to emphasize shadowing, which could be the most important in terms of clinical experience. Not even being an EMT will show you what being a doctor is REALLY like.