There are a lot of bad -- and beloved, in some cases -- history podcasts in which the author postures, makes bad jokes, and assumes you don't know much and only want to know a little more. Two exceptions to this are "The History of the Mongols", which is excellent and clear and takes a fair amount of concentration, and "Revolutions",* which takes an in-depth look to various European revolutions starting with the English Civil War. I've just gotten to Charles I leaving London for the last time (although he doesn't know it).
If there were ever a more shining counterexample to the Divine Right of Kings than Charles I, it has to be one of the monarchs who was actually insane or intellectually disabled.
* Revolutions' podcaster, Mike Duncan, is known for an earlier history of Rome, which I haven't listened to but hear is excellent.
If you like true crime that is dispassionate rather than overblown, I highly, highly recommend "True Crime Japan". The podcasters are gaijin living in Japan, and they do an excellent job of explaining Japanese customs and cultural aspects that are relevant to how crimes took place. These are not crimes that have been rehearsed over and over in English-speaking media -- no Ripper, Bundy, Lizzie Borden -- which makes them all the more engrossing.
All of the above are, of course, available on iTunes and other aggregators; I'm linking to the authors' sites.