My recommended German podcasts

Maybe your German is quite advanced and you would like to improve it or you are getting along quite well and are just looking for some suggestions.

If you are still a beginner, I recommend the "Slow German Podcast" from Annik Rubens. She offers podcasts for beginners and advanced learners of German - the text is written on her blog. She also provides a whole bundle of additional  stuff to learn in her online shop.
Annik Rubens is quite known in Germany, she was one of the first podcasters and is still very active in the podcast scene.
I listen regularly to her personal podcast "Schlaflos in München" and another one she makes together with Alex Wunschel, "Na Servus" (unfortunately there haven't been any episodes for some time but I am still hopeful that they continue sooner or later)

Two other entertaining personal podcasts are Mikrodilettanten and Not Safe for Work
although I think for a non native German speaker there is some challenge involved.

Maybe you prefer a more philosophic and ironic approach with Gunter Dück and Robert Kindermann.

Unfortunately not all of the good podcasts are continued, I really liked Chicks on Tour, two Abba cover singers from Munich who talked about what happened to them during their tours, but even though, listen to the old episodes, they are really funny.

Another type of podcast: A German guy, living in Japan, talks about every day life in this interesting country. Sometimes also interrupted for some time, hopefully he continues again with Kilians Podkost.

Another podcast I mentioned already is Staatsbürgerkunde where a young guy talks with other people, usually his parents, about life in the German Democratic Republic.