Downcast here.
Started using it when Apple butchered the music player in iOS5. Sooo glad Apple ruined the music player, I would have ignorantly stuck with the iOS4 player had they not changed it, when Downcast is a million times better and more convenient. Can't believe I physically synced with iTunes for podcasts for so long, uurgh. Downcast is easily amongst my most used apps.
As for podcasts, my faves are (I'm from the UK);
This Is Only A Test
The Vergecast
Guardian Football Weekly
Football Ramble
BBC World Football Phone In
TheGame
Weekend Confirmed
This Week In Tech (video)
There's others, but these are always top of my playlist. Used to like the Engadget podcast until all the crew left for The Verge. Of their replacements, Tim Steven's is very wooden and Brian Heater is the least funny person I've ever had the misfortune to listen too, yet peppers the podcasts with his "jokes". Awful.