Okay I'll try to narrow this down to my favs, and also to ones not already mentioned, because I subscribe to tons. They are in no particular order
Tech Related (gaming, computers, tech news etc)
*sorry that right now these are all gaming podcasts, usually I listen to more variety.*
EZ-Mode Unlocked: Gaming podcast, very casual, very funny. And don't worry, it is not yet another podcast consisting of "what are you playing, news, the end". They have a unique format that is a lot of fun, and involves the community. I've "known" the hosts on forums and the like for, oh, 4 years or so. They are awesome people, and very funny. There is an AMAZING community at ezmodeunlocked.com. Not only are there awesome forums (again, have known many of these members for years) but there is also an accompanying blog. Please give it a listen! Once you get to know them you won't be able to stop.
Gamers with Jobs: This is also a really great podcast, completely different feel from EZ-Mode. Intelligent conversation on interesting topics related to the gaming industry. I don't "know" the hosts or community like I do over at EZ-Mode.
Weekend Confirmed: Shacknews' podcast. I don't care about Shacknews really, but this is Garnet Lee's new podcast! Enough said.
Non-Tech Podcasts
PRI: To the Best of Our Knowledge: I love this podcast. It is so incredibly diverse. I mean, what other podcast addresses so intelligently and in such an enjoyable fashion issues ranging from Autism, Reviving Classical Music, Psychodelic drugs, Caveman (exploring the finding that we, modern humans, are 1 to 4 percent Neandertal), Reality, etc.
BBC All Things Considered: A great podcast that explores spiritual, religious, philosophical, and moral issues. Examples of past podcasts address issues such as Human Trafficking, Suffering, Prayer, and then episodes focusing on individuals such as Claire Bertschinger, Nicholas Evans (Pilgrim and Painter), etc.
Speaking of Faith: I know religion is kind of taboo to talk about on forums, but this is an incredible podcast that is so open-minded, thoughtful, thought-provoking, etc, that I had to include it. It is not all about religion (and by religion, I mean all types of spirituality, from Christianity, Islam, Judaism, Hinduism, Humanism, Native American Faiths, Buddism, Agnosticis, and Atheism) For example, there are episodes with titles like "Alzheimer's, Memory, and Being", "Mathematics, Purpose, and Truth", "Play, Spirit, and Character", and countless others. She interviews astronomers, theoretical physicists, religious leaders, controversial thinkers, etc. Krista Tippett is perhaps the best host I have ever heard. She asks deep, provokative questions, has a wonderful voice to listen to (I often listen to this as I go to sleep) and comes with an open mind and with an amazing amount of knowledge. This podcast does not advocate for any belief system; it is, as it's official description says, a conversation about religion, meaning, ethics, and ideas.
NPR: Wait Wait...Don't Tell Me!: A hilarious weekly current events quiz show. Check it out.
Ok, I'll try to remember to edit this as time goes by. Remember to check out EZ-Mode Unlocked!