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@tkoola Fresh Air and This American Life, if you count radio programs also available as podcasts. Those go back to the 1980s IIRC.
Heck, if you’re going to count radio-as-podcasts—I used to listen to old-time-radio and been thinking of picking it up again. That would mean I’m listening to podcasts dating back to the 1940s!
If you want to count only native podcasts, I think the oldest one I’m currently listening to is Dan Carlin’s Hardcore History, launched 2006.