Love to see lists of podcasts in these forums. It's such a fun medium.
Any list about UX that doesn't have Jared Spool in it is probably incomplete. :)
I'd like to humbly recommend the shows on the Spec network. Design Details is probably the best for this category, but every show on the network, to some degree, deals with common issues in both UX and UI design.
(Disclaimer, I am the host of Developer Tea and a cofounder of Spec.)
As Jon said, cain't forget Design Details Personally that's my favorite, as they seem to be the most human, authentic interviews and the topics tend to steer towards more early/mid-career advice
A little off the beaten path but perhaps relevant...
- I like Presentable (Jeff Veen), good guests and good questions.
- A few podcasts like 10% Happier (or mindful meditation oriented) helps me deal with personal bias and subjective narratives, which helps with design.
- Song Exploder can be incidentally informative because it's about iteration mostly.
- I used to listen to the Big Web Show, but Zeldman doesn't let anyone talk anymore.
I think you should definitely listen to this podcast:
Thanks for sharing, I didn't know 2 of them.