I pretty much listen to all gaming podcasts. My first and favorite, way back in 2006ish, was "Endgame Radio" (looks like even the archives are gone now.) It was an interesting combination of video game news and discussion alternated with an eclectic mix of techno, goth/industrial, and video game soundtrack music.
When the schedule for that got erratic i started listening to the various 1UP and GameSpot podcasts. When those were killed off/died off for various reasons i picked up Rebel FM and Weekend Confirmed. I then picked up RPGFan's "Random Encounter", the somewhat short-lived GamePro "Roleplayer's Realm", and the very short-lived "A Life Well Wasted".
I kept trying to get into the Joystiq podcast (when that was around) and Giant Bombcast, but they kept falling out of rotation because i just didn't have enough time to listen to everything.
There were numerous other little podcasts i tried out for awhile but either the podcast or my interest in it didn't survive in the long run. (The one non-gaming podcast in that category was the now defunct "ReadMoreSciFi")
Now days when i have the time (which hasn't been often for the last year or two) i listen to 5by5 DLC, Rebel FM, RPGFan, and the occasional Giant Bombcast (assuming none of those have been cancelled in the couple months since i last checked =P)
I tried looking for a FF14 podcast for awhile, but it's difficult since i got a late start on that game and i'm _still_ not up to date. I also spent a little while a couple years back trying to find a decent anime podcast or a second decent SF/F book podcast but didn't have any luck at the time. Perhaps if podcasts are really experiencing an explosion in popularity i ought to try looking again. (Not that i have time to keep up to date even with just my "current" podcasts.)