Recs.
Updated
Pocket Casts is a podcasting app that works for Android 2.3+. The verge gives a great rundown of the app here:
SpecsUpdate
Pros
Pro Very fast access to new episodes
From their website:
Pocket Casts utilizes a global network of servers designed to do the heavy lifting so your phone doesn't have to. Our servers check for new episodes and deliver the updates instantly to your device. Your phone doesn't need to check each of your subscriptions individually since our server did it hours earlier. This results in a much faster refresh and considerably less bandwidth use than other podcast apps.
Pro Remembers playback speed & starting position
You can set a 'start from' position for a podcast to skip a set number of seconds from the beginning of an episode. Great for when you don't want to listen to an intro you've heard a couple of dozen times before.
Additionally, you can also change the playback speed, to slow down fast talkers or speed up slow talkers.
Pro Vibrant aesthetics
Pocket Casts has one of the most colorful, pleasant to use interfaces.
For example, the app takes the most prominent color from the album art and colorizes the rest of the playback interface based on that color. This allows the app to stay vibrant and slightly different for each podcast.
Or the way it displays featured podcasts in a colorful mosaic made from album art, makes the whole experience of using the app pleasant.