I'm picky about my news apps, and have tried all the main web sites and the corresponding apps (CBSNews, CNN, etc.). The one I like best is BBC News.
Clean presentation of the different stories, with a smooth interface.
It has never crashed.
Nice feature: I can read the story or watch the video (if available), and if I watch the video, it comes up immediately, with no ads and fills the screen.
Two honorable mentions:
1. Zite -- This has many more stories than BBC, but it has gotten very buggy lately.
2. Pocket -- I use this to view a new web page. It takes five taps to convert a web page and view it, but eliminates all ads and displays the text in a nice readable layout.