NPR, formerly National Public Radio delivers breaking national and world news. Also top stories from business, politics, health, science, technology, music, arts and culture. Many NPR news and music stories are available for download. Simply click the "Download" link, next to the headline on a story page or in the program rundown, and a download will begin automatically.
Unfortunately, not all stories available for download. For certain special features like exclusive music tracks, live concerts you need a streaming audio recorder software.
Here's some tutorial on how to record live streams from NPR.org with NPR Radio Recorder.