Car talk
Not totally relevant, but there’s a pub in Liverpool called The Shipping Forecast, bit wanky but you know, any port in a storm. Anyway they play the shipping forecast in the toilets, and fuck me if it isn’t nice and soothing when it fills the silence as you wait for the piss to breach the porcelain.
At the moment I’m very much enjoying Paul Sinha’s Perfect Pub Quiz
What a clever wee dumpling he is
If satellite radio counts it was Drew Carey’s Friday Night Freakout, but he sadly is no longer making it.
Theme Time Radio Hour with Bob Dylan!
…which hasn’t been aired for years, so you’d have to download it. At which point it could might as well have been a podcast. But it is a radio show!
When I listen to the radio live (as I am doing as I write), I listen to music only, occasionally channels that have brief news every hour if I want to feel connected to the world.
In other words: Please reveal your approximate geographical location for data collection purposes.
They call those “podcasts” nowadays. But in the spirit of your question, I’ll say my favorite is Wait Wait Don’t Tell Me.