Since Google Reader is going to be shutting down on July 1st I've officially switched to Feedly. While nobody is happy about Google Reader shutting down it is pretty inevitable at this point and it doesn't seem like Google is changing their mind even with petitions to keep the RSS service open.
Switching to Feedly was pretty painless as you just your own Google account to login and Feedly will pull your RSS feeds in. Using Feedly for awhile I think it is a good RSS alternative to Google Reader. Feedly is fast, the design is nice, and you can change the layout to your personal preference. Feedly also features a nice app which works on both iOS and Android mobile phones.
Feedly used to run on Google Reader's backend but now Feedly has built their own API (application programming interface). This was launched on June 19th and the API was nicknamed Normandy. The Normandy initiative was built so that Feedly could run in a cloud environment while supporting several different apps that used to run on Google Reader.
While I don't think Feedly is a bad I don't like it nearly as much as Google Reader and still prefer it. One RSS alternative you could consider is The Old Reader which has got more of a Google Reader feel. I like The Old Reader for it's simplicity ease-of-use. However, it is not nearly as fast and snappy as Feedly. Also importing your Google Reader RSS feeds is not quite as straightforward. You will have to go to Google Takeout, download the XML file, and then upload it to the Old Reader. This was easy for me to do but might be hard for those that are not tech-savy. Of course if you use RSS feeds I assume you probably are tech-savy.
Since the developers behind The Old Reader work on it in their spare time it is understandable the product is not quite as refined as Feedly. I will probably play around with it more and see how I like it. Since I've switched to Feedly I've been using that mostly. Not sure I will be using the Old Reader because of the faults mentioned above. It still does have a loyal following and user base and I recommend you at least give it a shot.
Anyway I've switched to Feedly and think it is a good alternative for Google Reader refugees. (First world problems?) Still it will take getting used to and I'd prefer it if Google wasn't shutting down it's RSS offering.