I am fairly obsessed with podcasts. I find they're a great way to consume information and be entertained at times where other options aren't feasible. (It's hard to watch tv while mowing or read a book while driving.) Plus they're free, always generating new content, and can be educational. Here's what I'm listening to at the moment:
These are generally timeless podcasts I enjoyed but are no longer publishing episodes.
My podcast player of choice is Overcast. I'd consider this to be the best one, far and away from the rest. It's now free, so that makes it even better. I'd previously used Downcast, which was fine, but I don't find myself missing anything about it. It's iOS-only—sorry Android users (though there is a decent web interface that doesn't have quite the same features or polish).
I'm a little ridiculous when it comes to speeding up the playback. I'm around 2.25x normal speed (not counting Overcast's Smart Speed), which is probably a bit extreme. But it's nice to be able to condense time a little since the files are generally downloaded.