AntennaPod is an open-source podcast manager for Android 2.3.3 and above. It offers all the basic features you expect from a podcatcher, like streaming and downloading episodes, refreshing all feeds automatically or adding them to a queue to listen to them later. Moreover, AntennaPod lets you flattr podcasts and episodes from within the app.
So far the following features are implemented:
* Downloading and Streaming of episodes
* Variable speed playback (requires Presto Sound Library or Prestissimo)
* Support for Atom and RSS feeds
* Support for password-protected feeds and episodes