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Android tablets are great for listening to podcasts, and DoggCatcher is a great way to do so. Once you subscribe to podcasts of interest, the app downloads new episodes when they appear and handles playback simply. You can incrementally speed up the playback to get through long podcasts in much less time.
DoggCatcher has a good library of podcasts to help you find what you like, and you can search for specific shows right in the app.
In addition to handling podcasts nicely, the app can handle RSS news feeds, too. I've never used it for that, preferring to use it as my podcast app of choice.