It's hard to recommend stuff without knowing your tastes, but let me give you five from my huge podcast collection to get you started:
1. A Way With Words: Do you like language, the history it carries with it, and its place in culture? This is the podcast for you!
2. Cox & Crendor In The Morning: A somewhat risky suggestion; this is a fake morning show run by two fantastic idiots. Often hilarious, I suggest listening through the archives. I imagine this will be the most polarizing of my suggestions.
3. Hello Internet: A masterpiece of the 'two guys talking' genre. The cool thing is that both of these guys are super smart and in the same business (educational YouTube videos), but both are so diametrically different in their approaches to their work and the world around them.
4. How To Do Everything: NPR's comedy take on an advice show. Mike and Ian (of the amazing Wait Wait Don't Tell Me) investigate questions ranging from what to do if you are faced with a bear (advice that actually saved a listener) to finding the best public toilet in the world.
5. Radiolab: My favorite podcast of all time. The topic for a given episode could sound like the least interesting thing imaginable, yet, by the end of the episode, I'll find that topic amazing. This show is really about finding the wonder of our world, something we all need a reminder of from time to time.
I've got many more good suggestions on many topics, just let us know your interests!