Pocket Casts is the Android app I use and it's pretty good. It supports streaming or downloading podcasts and you can adjust playback speed, auto-skip silence, customize forward/backward skip button durations, etc.
I second Pocket Casts. It is good enough that I will probably keep using it instead of switching back to Overcast if/when I go back to iOS. (It has an account sync feature.) I paid $5 for it, similarly to the $5 I paid for Overcast.