Developer: NewsGator Technologies, Inc.
Price: free Download on the App Store
NetNewsWire has an unfortunate name. It doesn't sound like an RSS reader, and there is no connection between its name and its parent, the well known (and liked) NewsGator RSS service. However, the product is solid, and currrently the best choice for an RSS reader on iPhone until Google Reader completes its iPhone port.
To use the service, its highly advisable to first create an account by going to the Newsgator website. From there, its fairly easy (but not quite as easy as in Google reader) to create a list of RSS feeds. You can choose which display order you want to show the feeds in (by default its oldest first, which you will want to change), and wether to show the entire article or just the summary.
Once you do this, you can peruse your feeds in the reader app, which works remarkably well -- a significant improvement over, for example, the Google Reader website for iPhone. Read feeds are grayed out - immediately, and you can easily mark an entire page as read. The experience is zippy and pleasurable.
The only faults I have with the web app is the inability to add feeds directly from the phone. But overall, its good enough that I am going to be switching from Google Reader... for a few weeks.