While experimenting a bit with my iPhone, I found several of the best news sites on the Net actually have really good mobile interfaces. Often, the websites have better interfaces and more information than their iPhone app counterpart. In addition, these sites are likely to work well on Android and other mobile devices.
Here is the list:
On an iPhone, you can add a website to your desktop so it looks just like an app. To do this, navigate to the website in Safari. Then select the plus (+) and then "Add to Home Screen". This adds a an icon for the website on the currently selected page.