You Must Remember This (Slate): Karina Longworth's now-legendary podcast investigates the myths, depths and struggles of Classic and New Hollywood. Her series on Kenneth Anger is especially noteworthy. She is such a talented narrator, researcher and all-round storyteller. This is likely to stay at #1 for a while.
Team Deakins: a legendary cinematographer (Roger Deakins) interviews equally legendary professionals. What more do you want? Learn everything from working with actions sequences, to what a DIT actually does as well as shooting on film. It's a really great school for the budding filmmaker.
Little Gold Men (Vanity Fair): this podcast offers unparalleled industry insights, criticism and gossip about Hollywood's biggest releases, as well as news from the frontlines of key awards ceremonies and festivals. The hosts are witty, speculation is juicy and analysis is mostly sharp. It's also lovely to see an incorporation of the TV landscape into the discussion.
Happy Sad Confused (MTV): the sheer calibre of talent available on this podcast is impressive, from Daisy Ridley to David Harbour. I love how Josh Horowitz reaches far into the guests' careers to illuminate their present work.
Fantastic Geeks and Where to Find Them: this is a guilty pleasure. The hosts are lovely (some would say annoying) and conjure up that feeling of excitement when watching Star Wars for the first time. The show is obviously very Potter-heavy, however their discussions range everything from Lord of the Rings to the Avengers. A real must for geeks.