Giant Bombcast and Giant Beastcast for video game stuff.

Radiolab
99% Invisible
Revisionist History
My Brother, My Brother, and Me (comedy faux-advice show from the McElroys)
The 1099 (a good games industry interview show)
Important if True (the Campo Santo folks just talking about random shit, usually featuring robots and/or AI and stupid doomsday scenarios)
Idle Thumbs (those same Campo Santo guys talking video games)
Designer Notes (game devs interview podcast)
Friends at the Table (a tabletop gaming play podcast from Austin Walker and his friends--really great podcast if you're into that sort of thing)
The Adventure Zone (a more comedy angled D&D podcast from the McElroys)
The Easy Allies podcast (video game newsy stuff from the old GameTrailers guys)
Frame Trap (the Easy Allies in-depth sort of "what have you been playing" discussion podcast)

I will second My Brother, My Brother and Me as well as The Adventure Zone.

One that I have found recently that I like is The Rebel FM. It's a couple friends who work in the games industry just shooting the crap about gaming news and what they are currently playing.

Alice isn't dead
Limetown
S-town (must listen!)
Dev game club
Five thirty eight politics
Crimetown
Destiny community radio

(My politics skew center left, so do my political podcasts)

The weeds
Lovett or leave it
Pod save America

If you like ancient history, I recommend "The History of Rome". It's no longer current, but antiquity hasn't changed that much since 2012.

- No text -

The Destiny Community Podcast
Your Moms House Podcast (Farts and Big words)
Ten Minute Podcast (Start from the beginnning, absolutely worth it)

I… Listen to a lot of podcasts.

I organized this by the network, for no reason other then just giving some structure to it. No particular order.

RelayFM:

• Upgrade - Tech News show
  
• Canvas - Productivity Show
  
• Reconcilable Differences - Merlin Mann and John Siracusa talk about who they think and what make them them. a Personality show, lets call it.

The Incomparable:

• The Incomparable (pick and choose) panel discussions about nerdy media
  
• The Game Show - Lots of TV video and board games ripped off and recorded for audio format. It's funny more than gaming. A good transition for the Adventure Zone fans.
  
• TV Talk Machine - The Hollywood Reporter's chief TV critic talks weekly about "TV". The show has been rebooted a few times so there are some inside references to get through, but it's not so bad with that.
  
• Robot or Not - John Siracusa classifies different things as either being a Robot, or not. (and then the show expands after that to other issues of classification)

Radiotopia:

• West Wing Weekly - Weekly rewatch with a super fan and Josh Malina how joined the cast part way through the series. Lots of interviews with cast and crew.
  
• Song Exploder - Breaking down a song with deep analysis and history. Hosted by one of the hosts of West Wing Weekly. The one who prepares.
  
• 99PI - Mentioned by others.

NPR/APM:

• Ask Me Another - Comedy nerd and puzzle game show with Jonathan Coulton
  
• Wait, Wait, Don't tell me - Comedy news game show
  
• Hilarious World of Depression - Interviews with comedians who have depression.
  
• Wits - Think Prarie Home Companion with a more twisted comedy sensibility. Now defunct, but the archives hold up.
  
• Radiolab - Science podcast edited to within an inch of its life

MaxFun:

• The Flop House - The 2d best podcast on my list. 3 Friends who watch a bad movie, and then talk about it. The show starts rough, with bad audio quality and one of the 3 does not show up for the first dozen or so episodes. I say start with "a bullet to the head" and if you like it go back to the beginning. Also, along the way they guest host the Adventure Zone so you may have already heard them.
  
• Judge John Hodgman - People bring disputes to a fake courtroom of internet law. Interpersonal disagreements are settled by John Hodgman
  
• MBMBAM - Mentioned by many others.But, if you have not seem the SeeSo video version, it's free to watch right now and you should.

Indie:

• You Look Nice Today - The best podcast on this list. Now defunct, but just start at the beginning. I love it so much.
  
• Do By Friday - Merlin Man and some folks from Cards Against Humanity tried to start a Top Chef podcast, and when that failed it gave birth to a weekly challenge show, which itself barely holds together as they talk about tech and politics so much it barely leaves time for the premise of the show. Lots of running jokes, is give yourself time to become initiated
  
• Accidental Tech Podcast - Some nerds tried to make a show about Cars, but failed and ATP resulted. Weekly Tech news, mostly Apple.
  
• Dead Pilots Society - Pilot scripts that were rejected gat a table read.
  
• The Rebound - 3 tech writers got layed off from Macworld and made a weekly tech news podcast. More comedy and insulting each other then tech news, but the commentary can have genuine value.
  
• The Bungie Podcast - yep.
  
• Daring Fireball - The Audio director's commentary for the web site of the same name.
  
• Drunk on Disney - 2 of my favorite things - Booze and Disney Parks, hosted by Nerd writers and Dana Snyder. It's hard to recommend because it's so niche and haphazardly produced, but if you were to make a podcast just for me this would be a really valid attempt, so I want it to live. TO give it a fair shot start listening a year or two back.
  
• Jim Hill's Disney Podcast - Disney Parks News and history podcast
  
• WDW News Tonight / Today - Tonight is a goofy weekly radio show about Disney Parks news. Also weekly game shows. Tonight is a more professional panel discussion show.
  
• The Golden Horseshoe Review - Disney Parks fan Podcast
  
• Hypercritical - Now defunct. John Siracusa complains about stuff. Best episodes include the Nintendo Wii U set up episode, and "they got the wrong guy" 2-part on the Steve Jobs Bio. There's a good one on video game controllers too I think.
  
• Ready Up Live - Part of the fun is you never know if it is alive or dead! Just put it in the pod catcher and occasionally be surprised by a non-whispering CruelLegacy
  
• Guardian Radio - hmm. I really don't recommend it but I do because it's on topic and I listen every week? I like having a weekly Destiny News show, but there's so much that frustrates me about it, from the repetitive unfunny jokes (endless jerky boys impressions), to not listening to each other and either repeating things that were just said, or not understanding each other and arguing about things the other didn't say.)
  
• Ze Frank's video podcast - whatever that was called before we had the word podcasts

Do the Right Thing: podcast comedy panel game. Now a TV show in addition to the podcast.

No Such Thing As A Fish: QI researchers host an informative comedy panel show with no game element, where you learn things like that there's no such thing as a fish. Also now a TV show in addition to the podcast.

The History of English podcast: people ask me how I know so much stuff about English linguistics. It's because I spent $10k on a degree in it. I could have just listened to this podcast instead.

You're pretty well set on podcasts that you listen to every day or week, and Adam Carolla is hilarious, so I think these would just add a little bit to your life and they will be fun.

Oh, Glitch please from Red Vs Blue is an all right video game podcast. It's the only one I listen to.

It's not a Podcast, but if you want to have hours worth of audio to listen to, might I also recommend Halo 2 ARG I Love Bees Audio files?

http://www.thebruce.net/ilovebees

There's also the media that Blackstar and Narcogen (and Funkmon) put out on Rampancy.net. I stumbled across them on twitch playing through Alien Convenant on Sunday and it delayed my whole day by an hour and half.

TwiT

• All About Android - The Android experts keep you posted on the latest news, hardware and apps
  
  
• FLOSS Weekly - We show off free, libre, and open source software here each week.
  
  
• Ham Nation - Calling all hams! The ultimate amateur radio talk show meets here weekly.
  
  
• Home Theater Geeks - This is the show for big screen TVs to surround sound to the latest video tech.
  
  
• iOS Today - iPhone, iPad, Apple Watch or Apple TV, if it's iOS Megan and Leo show you what's new and what's cool.
  
  
• Know How... - Get the know how to make technology work for you.
  
  
• MacBreak Weekly - Get the latest Apple news and views from the top names in tech journalism.
  
  
• Security Now - Steve Gibson discusses the hot topics in security today with Leo Laporte.
  
  
• Tech News Today - Your daily dose of tech news featuring the top tech journalists.
  
  
• The New Screen Savers - "" is a variety show for tech on the TWiT network.
  
  
• The Tech Guy - Leo Laporte takes to the radio every weekend to talk tech and answer your questions
  
  
• This Week in Computer Hardware - Do you obsess about computer hardware? This is the show for you!
  
  
• This Week in Enterprise Tech - Keep up on the latest in cutting edge enterprise tech.
  
  
• This Week in Google - The latest Google and cloud computing news.
  
  
• This Week in Law - Join Denise as she discusses issues in technology law.
  
  
• This Week in Tech - Your first podcast of the week is the last word in tech.
  
  
• Triangulation - The smartest people in the world talking about the most important topics in technology.
  
  
• TWiT Live Specials - TWiT's coverage of breaking news, on-location events, and geek conference expeditions.
  
  
• Windows Weekly - Paul Thurrott and Mary Jo Foley talk about Windows and all things Microsoft
  
  
• TWiT Bits - Highlights from various shows on TWiT.tv.
  
  
• Radio Leo - A compendium of netcasts from the Chief TWiT, Leo Laporte.