Pocket Casts just today started a beta version of this service [1]. The paired Android/iPhone app can sync latest episodes as well.

[1] http://www.androidpolice.com/2014/09/26/pocket-casts-web-now...

Overcast by Marco of Instapaper fame has a great feature where it syncs your podcasts from the iPhone App to his web app at overcast.fm, so you can go back and forth between the two. It has been really useful in my experience