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Tunein Radio Pro
Tablets are good for listening to music in the background while doing other things, and that can mean streaming radio programs with TuneIn Radio Pro. This app handles stations from all over the world in every music genre imaginable. There is a simple preset system for saving favorite channels, and a local function that displays all radio stations in your particular area.
The Pro version allows voice control for listening to music hands-free.
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.
Google Play Music
I listen to music all the time on the Note 8.0 tablet and the Play Music app is very nice. The big display of the tablet makes it a breeze to search through my large music collection, which is stored in the Google cloud. Google's Listen Now service, which is Google's music streaming service, has a large collection and is as good as the recently launched iTune Radio service.