SERIAL
If you've heard of podcasts, you've likely heard of Serial. Yes, it's great and yes, it is one of the firsts to do that sort of formatted episodic podcast season, but it's not necessarily going to be your thing. Personally i much preferred season one, which is true crime in podcast form. Season 2 was great as well, but the story did not grab my interest quite as much. Definitely see if it pulls you in, and be prepared to be frustrated when you get to the end of the season and want more.
FREAKONOMICS
This is a podcast with one of the authors of the Freakonomics book, Stephen J. Dubner. while technically the themes discuss "economic" issues, don't let that disinterest you. It's an awesome podcast that is well produced and talks to interesting people and interesting things. Scroll through the archives to get a sense of some of the many cool things they talk about.
99% INVISIBLE
This is a podcast with Roman Mars, and honestly, I'm surprised I like it. It's about design and architecture, but pretty loosely. It's great to listen to - very well produced, and i'm surprised by how many of the topics I find really interesting. It did take me a little while to get into this, and certainly not every episode is a winner for me, but there is a huge range of interesting topics in the archived episodes.