DISCLAIMER: In My Humble Opinion or IMHO if you prefer.
These are the best video game related (occasionally vaguely so) podcasts in no particular order:
1. Idle Thumbs: These guys are extremely intelligent and knowledgeable about the games industry. All three work at major game companies (Chris Remo works at Double Fine and the other two write for Telltale i.e. The Walking Dead Series). They can sometimes come off as a bit pompous and elitist, but they back up their occasionally abrasive opinions with solid reasoning and concise facts. I’ve often heard them speak positively about a lesser-known game and subsequently seen the game absolutely blow up on all of the major gaming websites. A recent example of this sort of paleontological gaming "journalism" was their expositions on a game called "Cart Life." A game of intentionally mundane description, one would wonder how they even came across it in the first place. Nevertheless, after they spoke about it on their podcast, the game was covered by several major outlets soon after i.e. PC Gamer, Gamespot, and more. They’ve also uncovered (at least for me) games like Tennes, NIdhogg, Joust, Hokra, and others.
2. Polygon’s "The Besties": I’m sure everyone here knows about this podcast already but I thought I’d put it on the list because I think it deserves recognition for being quite exceptional. The chemistry of the hosts is one of the more appealing aspects of the show. Their banter is almost always hilarious and intellectually stimulating. All four guys have their own unique perspective and all have different specializations that come in handy when speaking about games in a round table format. For example, Russ Frushtick knows quite a lot about iOS games and he keeps up to date on the latest and best games on the platform. He always has something interesting to say about the newest games and he always has a good download recommendation. Griffin McElroy (I believe I spelt that correctly) is an RPG expert. He is very opinionated about the genre and has a huge well of knowledge from which to draw. This is a great show and I’m hoping Polygon brings it back for a new "season".
3. PC Gamer US Podcast: This is definitely one of the more traditional gaming podcasts. It highlights the recent news in the industry and showcases some of the newly released games. The hosts are incredibly knowledgeable on the subject of PC gaming and are quite diverse when it comes to their specializations. They have everything from EVE Online players to DayZ specialists. They have a nice aura of positivity to most of their conversations as well. Some may criticize them for being PC elitists, but it sort of comes with their territory. They also come with a wealth of experience in their field and are widely regarded to be some of the best minds in gaming journalism.
4. The Indoor Kids: This show is hosted by a husband and wife who are absolutely adorable. The husband is a professional comedian and his wife might as well be, because she’s just as funny as him. They always have new and interesting guests and they cover a wide array of fascinating topics. This is a non-traditional gaming podcast. They are definitely susceptible to long, drawn out tangents about ridiculous things, but they’re almost always entertaining and delightful. This is a whimsical show that should put a smile on anyone’s face, whether they are interested in video games or not.
5. A Life Well Wasted: This is more like a podcast miniseries, due to the fact that there are only six episodes. The host covers some fascinating subjects and also composes his own music to use as interludes and background. The first episode is definitely a must-listen. He covers what he calls "The death of EGM", that is the demise of Electronic Gaming Monthly. It is a fascinating and glowing portrayal of the once titan of gaming journalism. This series is more like listening to a documentary than a traditional podcast, but it’s definitely worth taking a look at.
6. Chet and Jon’s Reassuringly Finite Gaming Playlist: This is a great podcast with two dynamic hosts who cover the games they are currently playing and (mostly) enjoying. They are both professional games journalists and have many interesting things to say about all sorts of games. This is a nice "quick hit" podcast because it has fantastic pacing. There are never any lulls or parts of the show where there isn’t a lot of focus or direction. They keep a steady stream of interesting information and opinions coming at all times. This is a nice podcast to listen to while in the car or running, as you don’t necessarily have to finish it because it’s partitioned into small bites.
7. Rebel FM: This is a staple of any nutritious podcast diet. Polygon’s Arthur Gies is my favorite host on this show because he brings a somewhat skeptical, somewhat cynical, but always intellectual and critical perspective to the discussion. These guys always have something interesting to say about the latest news and games. This is easily one of the best video game podcasts available and almost certainly one of the best podcasts overall, games journalism notwithstanding.
8. Weekend Confirmed: I’m including this podcast on my list despite some serious reservations. I have a positive opinion on the show as a whole; however, some of the guest hosts are hit or miss. I won’t name names but it’s safe to say that this show exposes the fact that there are a few people in games journalism that aren’t in it due to their talent alone. The show gives a nice recap of the most recent action and, for the most part, the hosts are varied, interesting, opinionated, and intelligent. This is one of the more popular gaming podcasts and is definitely worth checking out.