This started with wanting to share my podcast list so...

Current Podcast App: Pocket Casts ($4)

I liked the app from the start, so I haven't actually tried any others. Check slant.co or alternativeto.net for free options. If you have a good podcast app, you shouldn't need the links I posted below, which is one reason why I just linked to the shows' main pages where available.

Podcasts Checked out:

In no particular order:

Podcasts to check out:

I'll keep it updated when I remember, or whenever someone prompts me for information, links, or corrections.