I am going to be testing out two possible replacements for Google Reader for my RSS feed browsing. Both will ask for permission to access your Google account to pull in your current list of feeds, then import it into their system.
The first, InoReader (www.inoreader.com), comes in a variety of formats. I will be testing the Chrome browser extention, the web version, and the iPad mobile version. I have initially set up the Chrome extension, and succesfully installed my feed list and even read a few posts. One advantage is you can get it to look like Google Reader, so there's less stress from figuring out how to read your feeds.
The second, feedly (www.feedly.com), seems to be primarily a mobile device app or browser extension. It also will let you sign in with your Google account, then import your current feed subscriptions. feedly has several ways to look at the posts, from Flipboard style "magazine" blocks to more traditional several line blurbs.
I will post an update after I've had time to work with each.