iOS Feed Readers
Whether you're using your iPhone or iPad, there's a variety of native feed readers available for iOS.
This iOS app provides the ability to synchronise with one of many web based providers, or to keep track of feeds itself. Supports Feedbin, Feedly, The Old Reader, Inoreader, Readability and Instapaper. (and more!)
Features an efficient swipe-based interface to power through your feeds, and image caching so you don't chew through all your cell data.
Recommended by You Need Feeds.
The native News app on your iDevice supports feeds too! You don't need to sign up for any services. Just add your feed to the app when prompted. Try it if you don't want to install anything new on your phone.