From the summary of my article, published today:
Podcast Lounge and Podcatcher are the two standouts here (though WPodder might be in the mix if it had been updated since early 2012). If you're happy to either stream podcasts as needed or to strictly incorporate podcatching into your nightly charging routine then the very pretty Podcast Lounge may well suit - it's certainly got the biggest directory for finding new content.
However, for podcast fans from other platforms (perhaps refugees from Symbian or Android), run, don't walk, and get Podcatcher. It's supremely flexible in terms of getting your feeds in, everything can be automated, your playback position in each programme is remembered and you can clean up your GB of podcasts when needed. Podcatcher isn't the prettiest solution here, but it's the one I keep coming back to and it's the one that most closely matches the best podcatchers on other platforms (e.g. Poddi and Podcatcher [no relation] on Symbian, or Doggcatcher on Android). Recommended.
You can read the full article here. You might want to grab a hot beverage first...
If podcatching functionality was one potential showstopper that has previously put you off trying Windows Phone, then I don't believe that this is still a barrier - there's certainly no shortage of software options to kit you out with listening!