iOS: Apple released a new app today for managing your podcasts. You can browse the iTunes library, subscribe to your favourite shows, stream or download individual episodes, and sync them with iTunes.
iOS' podcast support has always been pretty crappy, which is why we recommend using Downcast to manage your podcasts. Apple's new app is pretty good though, offering the ability to stream or download individual episodes and keep track of your listened episodes through iTunes sync. You can also increase the speed of your podcasts, turn on a sleep timer to stop playing after a certain amount of time, and more. We still prefer Downcast for its advanced per-show settings, but if you use iTunes for podcast listening, this app will make you very happy.
Podcasts is a free download for the iPhone and iPad.