Mission Log - if you like Star Trek, you’ll probably like this. I think it’s a scream.
I’d also like to offer The Drabblecast a free plug. Strange stories by strange authors for strange listeners. Plus, August is Lovecraft month!
WTF with Marc Maron
Mohr Stories with Jay Mohr
The Nerdist with Chris Hardwick
Kevin Pollack’s Chat Show
The Adam Carolla Show
Good Job, Brain - pub-style trivia and interesting factoids.
Classic Loveline - replays of the radio show, circa mid-90s. Takes me back to high school.
Those are the three I actually listen to. I’ve dabbled in others, but there’s a new ACS nearly every day, Classic Loveline updates a few times a week, and GJB updates at least once a week, so just these three are still more than I can keep up with.
Since it hasn’t been mentioned yet, I’ll add “Doug loves movies”. Dumb yet entertaining.
And if you are looking for some Halloween scares, there’s always “The NoSleep Podcast”
Ever watch Jon Eats Carrots? Video of a guy sitting there, eating carrots.
Aside from various things already mentioned, I’m quite a fan of No Such Thing as a Fish, a weekly podcast from the QI elves. Each of the (usually?) four panelists starts of a segment of the show with their favorite fact of the week, and they banter around from that, bringing up whatever related facts come to mind and generally chatting. It’s fun stuff.
Just recently started in on the new Life of Caesar podcast, which seems to be from one of the guys who did Napoleon 101 years ago. Like that podcast, it’s not exactly neutral; these are a couple of guys who are unabashedly pro-Caesar. I’m a sucker for ancient history, though, and I’m aware of the bias. They’re a bit too inclined to joking about, as well. In general, it’s good enough, if not spectacular.
Oh, someone mentioned The History of Rome. The guy who did that has (after a long hiatus) come back w/ a new series, Revolutions. It does what it says on the tin, exploring various revolutions throughout world history. It started w/ the English Civil War, moved on to the American Revolution, and is presently deep in the early stages of the French Revolution. If you enjoyed his dry humor and general approach from The History of Rome, you’re likely to enjoy this as well. Also, he got much better license-free music for this one.
99% Invisible is quite good also. Each fairly brief episode explores something about design. The one that comes to mind at the moment dealt w/ the attempts to design markers for a storage facility for radioactive waste; they would need to be understandable tens of thousands of years into the future, when any modern language may very well have been lost entirely, and also needed not to incite curiosity that would cause people to, y’know, dig it all up. (Personally, I think the best idea is to stick it somewhere we’re unlikely to have any cause to dig in the first place, and not mark it at all; any marker will tend to make curious humans curious.) Skip the credits, as the host, Roman Mars, likes to have his 6-year-old son do some bit in them. OTOH, if you’re not like me and you don’t hate “adorable kids”, this might not bother you.
I’ll give The Incomparable and (one of) its sister podcast(s), TeeVee, an honorable mention; basically, it’s a bunch of geeks sitting around discussing geeky things. They’ve fallen into a “draft” format for many of their episodes, probably because it’s easy; basically, there’ll be some topic–say, best Star Trek episodes–and they’ll go around the metaphorical table, with each guest choosing one and talking a bit about it. They also do single (or several) topic podcasts on books, comic books, movies, old movies, etc; be aware that they’re not particularly concerned about avoiding spoilers, though they do usually “sound the spoiler horn” before they go there, so you can click off and save it for later if you prefer. I’ve gotten a handful of excellent book/comic book recommendations from these guys, and they’re good fun. The Star Wars episodes are worth going back for, as are the Indy Jones. The sister podcast, TeeVee, is immediate reactions to certain television shows–at the moment, they’re doing Sons of Anarchy and Doctor Who.
Most of the rest of my podcasts are either just radio shows, like Wait Wait and Radiolab, or “special interest”–professional wrestling and English football. If anyone’s curious, I can list those too, but I’m guessing not. 
It’s a limited series (8 episodes), but particularly if you’re a fan of Comedy Bang Bang and/or Andy Daly, I highly recommend his Podcast Pilot Project. Each one is a mock “pilot podcast” by a different character of Daly’s from Comedy Bang Bang.
They’re all funny, but the “Travel Bug with August Lindt” episode in particular made me nearly incontinent.