There are many great science shows around, NPR's Science Friday being one of them. However, I find WNYC's Radiolab to be more of a must-listen because of they way they are able to find an over-arching story from seemingly disparate interview clips or even show segments, for the extra content they inject into the podcast, and how they are willing to go beyond science towards topics such as art.
Radiolab is hosted by Jad Abumrad and Robert Krulwich. Jad is not afraid to push the boundaries of production. I've heard people call the show "over-produced", but that kind of gives the episodes their own style; it doesn't take long to know you're listening to an episode of Radiolab. Sound effects are liberally used, but they always seem relevant to the story, rather than superficial. Jad also uses the technique of having a guest do a self-introduction either part-way through an interview or to mimic the host ("So we talked to Joe Such-and-such" "My name is Joe Such-and-such"). It never feels like you're missing out on the identity of who's talking, as if the first part is to draw you into what the interviewee has to say and then you're given the context of who it is and what he or she does.
Robert, an NPR science correspondent, is an excellent storyteller. He's very good at taking different themes and pulling them together in a larger, overarching context. Both he and Jad are good at making interviewees comfortable and seem to be able to draw out good stories. Of course, there are times when a lot of editing goes into making the interview sound good in the show (they did a behind-the-scenes episode playing before and after clips) but in the end it's still about the story.
A great example of how a show flows to a conclusion was their latest broadcast show, Stochasticity. I'll try to explain the stories in generalities to not spoil things if you haven't heard it yet, but the first story is not only about a coincidence, but a mind-blowing set of coincidences. Another story is about probability and randomness, and how one's perception of what would be random can be very different than reality. The best part of the show, however, expands on that perception and how it's human nature to always to find the most interesting part of a story, even to the point of ignoring facts which would make the story somewhat pedestrian.
Even after the show was aired, Jad and Robert weren't done with the topic. A couple weeks later the podcast feed had a follow-up to the Stochasticity episode which not only expanded on one of the stories (about the likelihood Joe DiMaggio's 56-game hitting streak), it even touched on whether little decisions made during the day can be predicted or if there's randomness even there. It's not only this kind of episode which builds on previous ones, but other podcast bonuses (interviews, speeches, even a promo they made years ago which was turned down by Ira Glass) which make it worthwhile to subscribe, even if you happen to catch the program on the radio.
Radiolab is not afraid to go beyond science, and one place they've explored often is music. One featured the music Zoë Keating, a cellist who uses a box to layer multiple tracks while she's performing, making it sound like an orchestra. Another was Juana Molina, an Argentinean singer who mixes acoustic and electronic instruments along with vocals.
Even given the strong storytelling, the podcast's extra content, and the willingness to not stay strictly in the realm of science, the show wouldn't hold together without the chemistry that Jad and Robert have. In some ways they're opposites (young vs. old, producer vs. correspondent) but that contributes to their ability to present various sides of a topic. Some of it may be scripted, but they play their parts well and help to make the show a complete package.