As the chief creative officer of Thing 12 Games, I need to stay up on all that is going on in the game industry...so I listen to a LOT of gaming podcasts. Vox Republica is a *really* great board game podcast, for several reasons.
1. The reviews they do always seem honest and reasonable, and they call out their own personal biases when there is a game type they don't personally enjoy. They also don't trash a game, because of those personal biases (hey, let's be honest...we ALL have them, and there is no game that works for EVERY player out there).
2. Their discussion topics are really thoughtful, and interesting. They dive into game topics that I don't often hear in other podcasts, and have contributors be a part of that discussion. These are always insightful, informative, and thought provoking.
3. They do a pretty decent job editing their show. So far, I haven't heard some of the more annoying and distracting things that I hear with some podcasts. They appear to take their time to deliver good content...which is a way of saying they appreciate their audience and care about putting out a good product.
So if you're looking for a podcast that has some meat to it, something that will feed your interest in the hobby in interesting and unique ways, I highly recommend checking them out.