PodGrabber

PodGrabber allows you to easily find, grab, and play the latest episodes of your favorite podcasts. It supports modern android file permissions and stores episodes in the location of your choosing. Since you pick where to store the episodes, you can directly manage your library. Batch download features allow you to easily keep a fixed number of episodes. The modern UI is fast and responsive, with a rich set of features. (Be sure to long-press and "swipe" to reveal additional features.) It also supports launching playback of downloaded episodes in your favorite external audio player.