Many of our readers are mourning the impending loss of Google Reader, which will cease to function on July 1. The folks at Zite have a kinda, sorta replacement that can be used from within the free Zite personalized news app.
Zite has always been a bit of a hybrid, allowing you to access your Google Reader feeds manually, while providing the extra Zite-selected news, based on your interests.
Here's how to bring the feeds in: Link your Google Reader account by clicking on the magnifying icon in Zite. You'll find an option for Google Reader Feeds in your Quicklist.
The Zite developers want you to understand the Google Reader selection will only be found after you've restarted the app or added another category, something Zite will fix in the next release. Also note that not every RSS feed is currently indexed by Zite, which will improve over time. There is no folder support, but it is being worked on, and there is no ongoing syncing with Google Reader.
The Zite solution is not perfect or complete, but should please some soon-to-be orphaned Google Reader fans.
Other options on iOS are apps like RSS Runner and the TLDR Reader, along with Reeder and Feedler. If you want a wider landscape than Google Reader feeds provide, I'm a daily user of Flipboard and the Pulse News app.