I listen to them mostly when cleaning and driving.
another good one "Kermode and Mayo Film reviews " from the BBC
I LOVE podcasts. I subscribe to many, but only listen to a few. Not enough hours in the day!
NPR’s How I Built This- how people with ideas turned them into businesses like Instagram, stitch fix, dyson vacuums, stonyfield yogurt, etc
As to when I listen- when I walk the dog, or working around the house mostly.
I’ve recently been soaking up When Meghan Met Harry. All things royal wedding. 
Also, I recently threw in the towel on the Apple podcast application. iOS 11 version was so awful. After 3 weeks I kept accidentally deleting subscribed podcasts and was frustrated with so many clicks. I’ve switched to Overcast, and am much happier.
I listen to the Young House Love podcast. They are also bloggers about DIY, design, and home stuff. The weekly podcast is light-hearted. In the warmer months, I listen while I walk the neighborhood. Or on the treadmill.
Serial (in-depth reporting of a true-crime, podcast equivalent of the Netflix series, Making of a Murder) was really good.
I love the other suggestions.
Thanks for all the wonderful suggestions! I have a long drive coming up and will check some of these out, particularly the history-related ones.
I used to check long books on tape out of the library for lengthy solo drives. Lately I’ve been listening to lectures from The Great Courses, which can be pricey but are great company.
Another food science podcast I like: Gastropod - so interesting!
Also, @MIMomma , I downloaded a couple episodes of Young House Love - looks like something I’d like!!
This American Life
Revisionist History with Malcolm Gladwell
Invisibilia
Planet Money
Hidden Brain
Cooking Issues
How I Built this
HiddEn Brain
The President’s InBox – really great explanation of a single issue by experts, but not boring or partisan
Science of Happiness
Lore (altho his voice gets on my nerves)
The Allusionist – very short, but all about words
The Gist
What Should I Read Next – has good information but man, sometimes her voice…
I like Hidden Brain too. It’s an NPR podcast, about an hour long, and goes deep into issues of how the human brain affects our behavior.
I also love The Daily (NYTimes). It’s usually less than 1/2 an hour and manages to give in depth coverage of one current issue.
At the end of the year, they replayed their most popular episodes and featured updates about the people concerned.
The episode from 12/27/17 was pretty amazing. About a young man who was raised to be a white supremacist but then he went to college. They don’t mention the college by name but it was the New College of Florida.
The episode from 12/28/17 was also amazing. Not often that podcasts make me cry, but this one sure did.
All on NPR:
It’s Been A Minute with Sam Sanders
Pop Culture Happy Hour
CodeSwitch
NPR Politics
Rough Translation (but there haven’t been any new episodes in ages)
1A with Joshua Johnson (This is actually a broadcast show, but I usually listen to it via streaming after the fact)