PodBox

PodBox is a completely free, no strings attached, disable-ads-if-you-want, full-featured podcatcher!

It lets you:
-View schedule of your subscribed podcasts.
-View play and updating history
-Add and view bookmarks (time stamps)
-Import and export data (Including OPML, of course).
-Auto-update feeds and auto-download new episodes
-Change color theme
-Set sleep timer
-Set wake-up alarm.
-Favorite podcasts
-Log into services for specific functionality (Like auto-share to twitter, use pocket as a podcast feed, or auto-backup to Dropbox)
-Add folders as podcast feeds.
-Use YouTube channels as podcast feeds (And also stream YouTube videos)
-Expand functionality with scripts. (Like expanding feeds, showing YouTube subscribers of YouTube feeds and much more)
-View nerdy stats.
-Search iTunes, YouTube and much more
-Play "Lazy listen", for those days you just want to listen to something at random.
-View twitter activity directly in podcast feeds.
-And much, much more!

That, together with the expected functionality (The app saves where you last were, you can manage and add podcasts and episodes, video playback, etc).

PodBox also gives you the ability to tweak and customize the way it works, looks and behaves.
Oh, and did i mention that it's free?

I've got a lot more lined up for the future, in terms of features, and i'm always open to suggestions and feedback, and the app will get an update every week to address issues. So expect it to evolve and improve quite rapidly (Or, as rapidly as one person can make it).

---App permission rundown---
-Modify or delete the contents of your USB storage - Used for storing images for every podcast you've subscribed to, podcast audio/video you've downloaded and some cache files to offload some online actions.

-Full network access - The full network access is for streaming and downloading podcasts, as well as images for those podcasts. It also uses this permission to get podcast info, podcast feeds, to send tweets (If the user is logged in) and to send and reciever info to the PodBox server. This is a very important permission.

-View network connections - It uses this permission for knowing when to not waste your mobile data, and to know if internet is available so that the app can resume online actions right away.

-Pair with Bluetooth devices - This is a permission that media control requires. This app uses this mainly so that the button on your headphone works.

-Control vibrations - Is used for some notifications. Not a very important permission.

-Prevent phone from sleeping - Used for background actions (Like the auto update feature) and for video playback (Wouldn't want the phone to fall asleep while watching a video).

-Wifi wake lock. Is required for the app to be able to change the wifi state. This lock is there to make sure that the internet doesn’t go away while the app is updating feeds in the background.