AntennaPod is a free and open-source podcasting app for Android that allows automatic downloads of podcast episodes.
The interface is simple with a listing of your subscribed podcasts on the homepage. The app displays the number of episodes and the date when the last episode of a podcast was aired.
You can set the playback to pause when headphones are disconnected, adjust playback speed and also specify the refresh interval for feeds. There is also the option to enable usage of mobile data connection for updates if required. More importantly, the app also lets you choose the folder where you want to save podcast episodes – you can save everything on external memory card to save precious internal storage.
There is also a desktop widget to control the episode player without opening the app.
You can import OPML files or add your favorite podcasts by URL, select the episode of choice and then download or stream it. If you want to download the episode later, you can add it to your download queue. Another issue is that if you remove the feed, all the downloaded episodes also must be removed.
While the app is currently in beta, it is ad-free.