This thread needs a bit of a kick (unless there's a more recent one I can't find).
Current faves.
Comedy:
Athletico Mince - Bob Mortimer and Andy Dawson. Sublime BM silliness and no more than 9% football talk (that was a promise from the earlier shows but they don't get anywhere near that now). I've come close to having to pull to the side of the road and stop when 'Peter Beardsley' reads from his joke book. Top of the list for a reason.
That Peter Crouch Podcast - Closer to about 90% football. Behind the scenes look at the pro football scene, through PC's varied career. The blokey bonhomie may pall after a while, but so far PC has been a revelation.
A Very Fatal Murder - From the Onion people. The second series has just started, the first series was a pitch-perfect satire of all of those real crime podcasts (looking at you, Serial I).
Brian and Roger - a sometimes painful listen, sometimes funny, about a fictional one-sided relationship between two losers, one highly manipulative and always on the make, the other friendless but wanting to please. As revealed, exclusively, in the form of voicemails between the 2.
The Beef and Dairy Network - not what it sounds like it might be, which is partly where its appeal lies. Quirkily funny most of the time, but sometimes, for me, the flights of fancy fly too far away.
Non-British politics (I find the British variety too depressing) and History:
The Rachel Maddow Show - taken straight from her MSNBC tv show. Daily updates on (mainly) Trump and GOP shenanigans. She takes you through the latest and upcoming events, always with a view on precedent, or absence thereof, with a brief interview with someone, invariably from the left, to explain the finer details. Ads have just begin to creep in, but they're short and are limited to MSNBC trailers.
Pod Save America - Youngish guns from the Obama Whitehouse. The shine is beginning to tarnish a bit, and the show itself together with the interviews are a little too long for me so its dropping down my pecking order a little (so why it's in a list of faves, I'm not sure).
Conflicted - a 6-parter (now finished) on Middle East politics and conflicts. Two people talking through and opining on, in turn: 9/11, War on Terror, Iraq, Yemen, Syria, and returning jihadists. The 2 people being Saudi born ex-Jihadi turned MI6 spy Aimen Dean, and American ex-monk/current writer Thomas Small. I learnt a lot.
The British History Podcast.
Up to ep 315 and still only on AEthelred! 20-odd minutes at a time, sometimes washing over me, sometimes not (so don't test me on anything). One of those 'I've started so I have to keep going now'.
Other regulars, not quite reaching the level of 'fave':
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538
The New Yorker Politics and More
WTF with Marc Maron (very dependent on interviewee)
Various Pappys formats
Slate Political podcast
BBC Profile
In Our Time (depends on subject)
The Cycling Podcast (except for days following boring Giro sprint stages)
Flammecast
The Horne Section
The Bugle
Adam Buxton (depends on interviewee)
RHLSTP (ditto)
BBC Witness
Inside the Comedian (improv interview on fictionalized version of various comedian's life)