I listen to a lot of podcasts about poetry, about writing poetry, about writing in general. But I also get a lot ideas from listening to podcasts concerning other creative people, their processes, their lives, etc. Here are a few I recommend:
1) WTF with Marc Maron. This is an interview show focused on comedians. I find it extremely compelling, particularly the parts about people's career paths, their ways of being original and/or finding original material, how they perform under pressure, etc.
2) Meet the Composer with Nadia Sirota. Sponsored by WQXR New York, this show is an interview format featuring contemporary composers and showcasing their work. I love hearing about the problems they encounter in composition and how they go about solving them.
3) Radiolab hosted by Jad Abumrad and Robert Krulwich. I've raved about this podcast before, and its still great. Stimulating science stories for everyone. New material to bounce around in your brain. I've had several poem ideas come from what I've heard on this show.
4) The Arcade the podcast of Hazlitt Magazine, hosted by Anshuman Iddamsetty. This show from Canada's Hazlitt Magazine weekly interviews someone from popular culture. Often it's someone literary, which is useful, but which doesn't necessarily fit the category of this list. It's the other interviews, particularly the cartoonists, that have surprised me with comments that I've found helpful in considering creative problems of my own.