Wow, didn't consider this until your post. Losing Listen would be a big hit.
Can anyone confirm that the Android Listen app will cease to function (i.e. refresh your existing feeds) once Google Reader is shut down? Am pretty sure that it relies solely on Google Reader's "Listen Subscriptions" tag for refreshing your podcast feeds, so that's definitely another gap that needs filling.
I think it will. Google Reader was key to Listen. I've been using BeyondPod since Google stopped supporting Listen. It works with Google Reader just like Listen did. It's disappointing that such a key feature will be lost. Does anyone know any Podcast apps for Android that supporting syncing feeds like Listen/BeyondPod did with Google Reader?
I have been working on a river of news style RSS/ATOM/RiverJs client in the past few months (GPL3 license).
The project site is here http://rivers.silverkeytech.com and you get the app here http://goo.gl/kShgp.
The app is a bit young but it is maturing rapidly. I deploy a new version every two weeks or so. The next update is due in a few days.
Google Listen was killed off in August 2012:
http://googleblog.blogspot.com/2012/08/giving-you-better-goo...
It still continues to work and be used though, so GP's question is relevant. I think it can still work without it, but I'd be surprised if it's superior to all of the other free alternatives in the absence of Reader.
It works from the browser, including mobile browsers, and native apps are coming. There's also an OPML importer, though currently experimental, and subscriptions can be consumed as OPML, RSS, etc.