I'll save the shameless plug for the very end, but let me give you a few that I have come across in my research while trying to figure out how I wanted to structure mine.
First off, I guess it depends on what type of medicine that you are interested. Do you have any idea or are you just wanting something generic?
The Dr. David Geier Show - This is a great show that is released every Monday. If you are a sports nut as well as enjoy medicine, I think you'll really like this episode. He is VERY easy to understand but isn't afraid to use medical vernacular. Also, every week he talks about sports stars and their recent injuries. This is one that I listen to every week!
EMCrit Podcast - Dr. Weingart is VERY well known in the Emergency Medicine podcast world. His podcasts are very informative though may be a little over the head of people that are just starting in medicine. One thing that I really like about his podcasts is that his opinions are very well rooted in literature, yet he is consistently challenging the way Emergency Medicine practice. This is a good podcast to listen too, especially if you are interested in EM, however it may be a little tough to follow if you are new to the game.
A Gobbet O' Pus - If you only have a few minutes to listen, this is great way to pick up a bit of good knowledge! Most episodes are only 5-6 minutes long, but don't let the length fool you! Each episode is jam packed with information from the world of Infectious Disease.
Ultrasound Podcast - This is actually a video podcast so it may be a little tougher to listen to on the go. Sometimes the capacity of the ultrasound is often underused, but these guys are determined to change that! Subject matter is fairly broad and easy to enjoy!
The Lost In PreMed Podcast - I'm not going to shamelessly plug this too much, but I would like to throw my name in the hat while you are searching for something to listen for. This podcast is targeted at premed students to help them through the riggers of the premed journey. The show touches on everything from MCATs and interviews to volunteering and shadowing. There is also a medical term every episode as well as other little anecdotes.
Whatever you take the time to listen too, I think it will benefit you to get in the culture of medicine. Although it may be a little overwhelming, listening to what the "big boys" listen to could help you in the long term. Who knows...it may be a little inspirational too!