Serial is a weekly podcast from the makers of This American Life. It's been running for just over a month so we're only seven episodes in but it's already top of several iTunes Charts. It examines the true story of the 1999 murder of Baltimore school girl Hae Min Lee and asks if the right person was convicted?
It's think it's fantastically put together and the format is the perfect medium to examine a single case in the detail required. I've recommended it to every single person I know and everyone of them who's picked it up has become hooked like me. I really recommend it. Also I find Sarah Koenig's voice incredibly soothing (but that might just be me).
You can check out the website here - http://serialpodcast.org/
Alternatively here's a link to their soundcloud page - https://soundcloud.com/serial