Describing themselves as a "re-imagining of audio drama," The Truth is a podcast of short, original stories. Even the vaguest settings in The Truth create vivid scenes. If you like This American Life or Snap Judgement, you'll probably love this. It's the same great storytelling, only fictional. A few of my favorites are Interruptible, In Good Hands and Keep Running.
Sunday morning are best spent in the park with A Prairie Home Companion's news from Lake Wobegon, "where all the women are strong, all the men are good-looking, and all the children are above average." It's simple, and sometimes that's all we need.
BBC Radio 4 is filled with radio dramas old and new. It doesn't seem to be available on demand right now, but I used to listen to Red Dwarf. It has audio dramas for sci-fi, crime, politics and thriller with plenty of other common topics thrown in. Radio 4 also does special broadcasts of popular stories and books. I don't listen to it much anymore, as I prefer the convenience of podcasts now.