I have a few news and reviews podcasts, and a friend's podcast ("Everyday Einstein", a weekly podcast by someone who went to grad school with me), but I'd thought I'd review two of the podcasts that are a bit quirkier.
Tea and Jeopardy, hosted by Emma Newman, co-written by Emma and Peter Newman
The Premise: Emma Newman interviews various folks in the greater science fiction and fantasy sphere. There is tea, and pastry, and an exotic locale scouted by her loyal butler, Latimer (played by Peter Newman). And by exotic, we mean anywhere from the back of a roc to the Mesozoic, to an abandoned city that turned out to be infested by zombies. The 'and Jeopardy' part comes in that, after the interview, the guest invariantly has to escape some peril in order to not die horribly. (It's generally assumed this is because, while Latimer has many butlering skills, he's also got some evil desire to see most of Ms. Newman's guests dead.)
Why I Like It: I like the juxtaposition of the interviews with an ongoing story. Guests don't often reoccur, but they can make impressions -- I recall one agent escaped the Coliseum in Rome by controlling lions and convincing the locals she was a minor goddess, and her grudge against Latimer has come up several times.
Rachel and Miles X-plain the X-men, hosted by Rachel Edidin and Miles Stokes The Premise: Two geeks start a chronological (with occasional exceptions for guest interviews) discussion/book club for the X-men continuity. While you can get a decent sense of what is actually happening plot wise, you also get the commentary from two long-time readers and discussion of things like character arcs and so on.
Why I Like It: It's like the weirdest book club ever, with two people who are hilarious. There is serious stuff like the talk about portrayals of various sensitive topics (like 'how well does the metaphor of mutants as a persecuted group hold up and where does it cover up real life whitewashing and so on') to silly things like adopting random side characters as favorites and inventing fan theories that range from 'less weird than some actual canon' to 'designed for a laugh'). Plus, you know, outlining the actual plot of the comics, with some awareness for things like fans who might be getting into the comics from the movies or pop culture. (Like talking about when Magneto became something more than scenery-chewing supervillain, or talking about how Rachel and Miles have slightly different thoughts on Apocalypse depending on when they first encountered him.)
It's a shame that Rachel and Miles set the scope to only this part of the Marvel Multiverse, but... can you blame them? (They are currently at the mid 1980s as of episode 64, and that's with condensing all of the Silver Age into a few episodes. On the other hand, they now have three books involving X-characters, so their speed slows.)