For music I find Pandora to be indispensable. This is probably my most used app of all; it completely replaces my car radio. It allows you to create music stations from genres, artists, or songs. These stations are centered around whatever you select, and after a bit of training with the thumbs up/thumbs down feature, these stations are quite enjoyable to listen to.

As far as news apps, I have found that the NPR app is my favorite, although this one depends highly on your political preference. NPR is very nice because it allows you to listen to the news and read articles simultaneously. In addition, the radio shows are often very interesting and thought-provoking whether they discuss politics or literature. That being said I find it quite obnoxious when the broadcaster reads in a perfect American accent and then uses a Spanish one just to say a name like Jorge.

For weather apps I prefer the free version of the Weather Channel app(although I am quite certain the paid version is better I like free stuff); however, I have heard that the Weatherbug app is also very good.