I very rarely listen to podcasts, but when I do the ones I try to keep up on the most are our very own Skill & Bones Radio and The Real Middle Ages. Along with these, the other one I try to keep current with (and am currently only about 3 months behind...) is:
Jay & Miles Xplain the X-Men: Weekly podcast where a couple from Portland who work in the comics industry go through every X-Men comic and dive deep into continuity starting with Silver Age stuff from the 60s and are now at the beginning of the 90s after 160 episodes, having branched out to cover New Mutants, X-Factor, and Excalibur with special non-continuity stuff and interviews with X-related comics folks along the way. Super entertaining, great information, and also lots of great analysis of the highlights/shortcomings of the older eras from feminist/representationally aware points of view.
I also have occasionally listened to a few episodes of:
The Kaiju-Cast: Focused on Godzilla and other kaiju with lots of good news and information, kaiju movie reviews, and kaiju-related music.
Intensify Forward Firepower: Star Wars Armada podcast by a group of dudes. Good analysis of tactics, new releases, and some tournament battle recaps. Some of the opinions should be taken with a grain of salt...
Scum & Villainy: It's been a while since I've listened, but this used to be the premier X-Wing podcast. If they're still running it, they did pretty much what the above guys did, but for X-Wing.