Pretty much every major site has their own (or several) podcasts, as well as myriad other series that cover games in various fashions and forms. While learning about the site-related ones is usually easy, exploring beyond those can be quite a task
Some of those may be ongoing and current, some may be short-lived or discontinued, but all offer interesting game-related listening
Beyond news and critique
Final Games - Developers and journalists (guests have included Jason Schreier, Max Tempkin, and William Pugh) discuss their desert island games
Checkpoints - Interviews with developers (ie Rami Ismail, Bennett Foddy, and Chris Remo) about the games that have inspired them and had impacts on their lives.
A Life Well Wasted - Essentially the “This American Life” approach to topics related to games
Top Score - Discussion about video game scores and interviews with composers
Designer Notes - Talking with developers about why they make games and other game design elements
Game Is A 4 Letter Word - Another NPR-esque series about games and gaming
Infinite Ammo - Interviews with various indie game developers
Three Moves Ahead - Discussion on strategy games and strategy game mechanics/design
Headshots - Discussion on the psychology of gaming and recent gaming news
History Respawned - Focuses on exploring the historical context and accuracy of history-related games like AC, Mafia, and more
Indie games/Focused discussion (single game per episode or multiple episodes)
The Short Game - Focused on games that can be completed in a few hours or days, mostly indie games across PC, consoles, and mobile
Check It Out, Comrade - Two indie games discussed each episode
Cane and Rinse - Each episode looks at a single game, from a wide spectrum of classic, recent AAA, and indie titles
Dev Game Club - Veteran developers play and discuss a single game across several episodes
Watch Out For Fireballs - Focused on older games, although some episodes dicuss more recent releases such as Dishonored
Twenty Dollar Gaming - Monthly discussion about a $20 game that the hosts play throughout the previous month
Roguelike Radio - In-depth discussion and analysis of roguelikes, roguelites, and roguelike mechanics
Script Lock - A series of interviews with various writers and developers, focused on narrative and writing, and how they intersect with game design
