Of the few applications I've tried for reading the latest news, my favorite is AP Mobile News Network. And, with over 700 user reviews on iTunes, it must be among the most popular. Best of all, it's FREE. The latest version has added advertising, but it's not intrusive.
What I like best is the speed at which it grabs the news. I'm using a slower first-generation iPhone, and when I select Top News, it downloads the latest stories and thumbnail images in less than 10 seconds. When you select a headline, the text for that story is already on your iPhone. The New York Times app, in contrast, makes you wait for the text to download each time you select a headline to read.
This was also very useful when I was using an iPod Touch before I got my iPhone. I'd grab the Top News and the Local News before leaving my house via my WiFi network. In seconds I'd have it, and then when I was out and about, if I had some time to kill I'd read the news.
You can grab the news in about a dozen additional categories, such as Showbiz, Sports, Business, Politics, Lifestyle, and Wacky.