Beautiful Anonymous is interesting. An anonymous person calls in with something that has happened in their lives and the host and they discuss it for an hours. Covers all topics, mental health, sex, race, religion. It's American (if that matters -but I would love a UK version)
Distraction Pieces with Scroobius Pip -again, I'm interested in a lot of the guests he has on, but he's a great host and a lot of interesting subjects are covered.
The History Podcast with Dan Snow are often about a half hours chat with an expert in a particular area of history and give great snapshots into topics I wouldnt have thought about otherwise -I've used this as a springboard to further reading on many occasions.
Griefcast with Cariad Lloyd -talking about death. I think it won an award recently.
My Dad wrote a Porno -absolutely hysterical although I think the first book is the best.
Off Menu with James Acaster and Ed Gamble -(mostly) comedians talking about their dream menu
This American Life -again covers a lot of topics and sensitively covered -the recent one about high school shootings in the US was excellent if harrowing.
Athletico Mince -Niche but proper laugh out loud funny, although I think you have to love Bob Mortimer for it to work.
Lore -A podcast about the Supernatural. Aaron is starting to run out of subject material now I think but the first 50 or episodes are really good.
if you like silly comedy game show type podcasts then Do the Right thing, Pappys Flatshare slamdown, Alex Horne breaks the news and Mister Gameshow with Mike Wozniak are all worth a listen.
I love The Adam Buxton podcast as I just really like his presenting style and his chats with Louis Theroux are often comedy gold -as were the ones with Richard Ayoade.
Joan and Jericha the filthy fictional radio agony aunts. Julia Davis is the driving force behind it and it really does go to some dark, but hilarious places.
I bloody love podcasts