Wouldn't you rather have a nice cup of tea?
I was really into the Adventure Zone which was Dungeons and Dragons by people who don't take it too seriously and spend a lot of time goofing around.
Reply All talks about technology and the internet, but is really engaging and accessible.
Welcome to Nightvale was recommended to me by someone on here, and that's been really good (in a weird creepy way).
How Did this Get Made? is one of many 'make fun of B movies' podcasts, but the hosts are usually funny. If I've seen the movie, I'll listen to it.
The Dollop is one I've discovered more recently. They cover weird American history. The guys have the personalities of morning radio hosts and can be kind of annoying, but the stories they cover are usually fascinating.
Don't believe everything that you read.
I take back what I said about My Favorite Murder. It was charming for awhile, but they got tiresome pretty quick.
There are three Harry Potter themed podcasts I really enjoy: MuggleCast, Alohoamora (Open the Dumbledor), and Speak Beasty (for the Fantastic Beasts movies.)
For the non-HP fan, Stuff You Missed in History Class is wonderful, funny, and touches on a wide variety of topics from all over the world.
The New Teacher Podcast is great for teachers both new and veterans. I enjoy listening to their interviews.
I listen to all of these though iTunes.
I was heavy into Jackson Pearce for awhile.
H3 podcast, tiger Belly, sometimes Anna Ferris.
There's a podcast called "Guys We Fucked" by these two girl comedians. It's pretty funny.