I haven't listened/watched to all that many, so of those few I'd like to mention...
Acquisitions Inc: The original podcast series was my first introduction to D&D (outside of references on TV and a few episodes of the cartoon) and I still hold quite a fondness for them. I've never enjoyed the live sessions as much, but that's just a different kind of performance.
Chris Perkins and Robot Chicken: A game run by Chris Perkins during his "DM to the Stars" days with some of the crew of Robot Chicken. Worth a watch. Perkins also did a director's commentary where he talks about the session, the adventure, and his thoughts on running the game for new players.
Critical Hit: The podcast from the Major Spoilers site. I learned a lot from the DM, Rodrigo, and overall an excellent bunch of players. I fell off at some point in the Feywild season.
Gamer's Haven: A bog standard D&D podcast from 2009. I only mention them because after looking them up I believe all their recordings are unavaiable, they played through Keep on the Shadowfell two (!) times, and I imagine only like 100 people ever heard them. Just an interesting footnote from the early days of D&D podcasting.