Since I'm a podcast fan, and since it was mentioned in another thread, a thread specifically on podcasts is probably well overdue. There are tons that are available for free, and it is easy to jump over any adverts in the free stuff. You can subscribe to get versions without adverts, where these often have bonus episodes for subscribers, but I don't bother since there is already more than enough for free.
I listen on my android phone and I've found that the Pocket Casts app (free) is ideal and is easy to use. The BBC Sounds app is fine, and if you listen in bed both let you set a 'zzz' timer - but if you don't set one in Pocket Casts it will stop at then end of the episode you are listening to, whereas BBC Sounds will keep playing any subsequent episodes automatically - so I prefer Pocket Casts, plus you can get BBC stuff via Pocket Casts. So, having searched and subscribed, you can build up quite a library very quickly.
In no particular order, and all these can be accessed via Pocket Casts, some of my favourites are:
1. 1940s/50s radio detective series containing episodes as originally broadcast, including some of the original adverts - these three are all produced by the same guy:
The Great Detectives of Old Time Radio, Down These Mean Streets and Stars on Suspense.
2. Fantasy fiction
The Truth, Drabblecast and Radio Rental.
3. US modern history/crime
Infamous America, Criminal, Going West and Legends of the Old West (which I loved).
4. General History
The History of Rome (starts slowly but gets better) and the follow up by the same guy (Mike Duncan) Revolutions (very detailed but worth close attention), The Rest is History and The Ancient World
That is just scratching the surface - worth a mention is A History of Rock Music in 500 Songs: deals with the people and social issues behind the records, and isn't always an easy listen, but worth the effort.
There are many many more!
