Well I see that the Co-optional podcast and Cox'n Crendor has been already covered.
I think you should check out also Let's Drown Out by our very own Yahtzee Croshaw and his friend Gabriel Morton. They recently seemed to have moved away to Let's Plays again but I feel like it's worth giving a shot the thing that already is there. It's more of a relaxed conversation while playing (and later watching) some old game. It might not be some kind of ground-breaking industry-changing podcast but I simply find the dynamic between Yahtzee and Gabe to be very enjoyable.
I don't know if you're interested in non-gaming podcasts but I also really recommend Hello Internet by CGP Grey and Brady. If you don't know them, then CGP Grey has a very popular educational channel. It's kind of hard to really pinpoint the focus of the channel: his two latest videos have been a short primer for the Lord of the Rings mythology and an explanation of the Single Transferable Vote. Now that latter one might sound particularly thrilling, but Grey manages to make it quite interesting.
Brady on the other hand is a journalist, who has a whole host of science channels whose focus ranged from maths to astronomy and physics and more. His videos are generally him conducting an interview with an expert regarding a certain topics (for example the possibility of multiverses).
Now this might make it sound like Hello Internet is some kind of science podecast for brainiacs but actually it' a fairly laid-back discussion of topics from everyday life and they often recommend interesting shows. FOr example it's thanks to them that I found out about the series Black Mirror and also my next recommendation which is the Serial podcast. Serial has so far made it through season 1. It's quite unusual to be honest. It's about a journalist's efforts to investigate a murder case from 15 years ago and whether the convicted, Adnan Syed, was the actual killer. Now, we're talking about an ACTUAL murder case here. Adnan Syed is a real person, currently serving his life sentence in prison and he has become something of an Internet sensation with people on Reddit investigating thoroughly his case.
And the last one is perhaps a weird one, but I just listened to the first of episode of the Deferred Gnosis Podcast. It's between a satanist and an atheist who have discussed the existence of spirituality and whether religion has a place in the modern and future world. I don't know if the satanist part might put you off but I found it personally quite interesting.
Well, sorry for the wall of text!
TL

R: Let's Drown Out, Hello Internet, Serial Podcast, Deferred Gnosis Podcast (only one episode so far though).