Last week some of my TED colleagues compiled a list of 45 podcast recommendations. This inspired me: here are my Top 12. (Why 12? Because it makes a nice grid, that's why.)
Though there are some great podcast apps out there, my favorite remains Pocket Casts. It's available for iOS, Android, Windows, and it has a Web player to boot, plus a bunch of other nice features, all wrapped in a clean, easy-to-use interface.