I started out with the Basic Brewing with James Spencer. The podcasts are really good with lots of information.
However, the last few months I've been listening to The Brewing Network podcasts. There are a few different podcasts. The Sunday Session is usually pretty informative if they are concentrating on specific topics, less so if they are just interviewing a brewery, but still good. Jamil and Palmer have Brew Strong, which just started recently and they have a few shows that are pretty in depth. There is also the Jamil show which covers brewing styles and has started doing clones of commercial beers.
My brewing has improved immensely since I started listening to podcasts.