Personally, I'm still in denial about losing my beloved Google Reader in the near future. The web-based RSS reader has been a standby ever since I started using RSS, and even when I used other services, like the great Reeder app on iOS, they ran through Google Reader to get their content.
But the times they are a'changin', and as of July 1, Google Reader will be gone for good. Reeder has gotten out ahead on this one, and just recently pushed out an update for its iPhone version that liberates the app from Google Reader's clutches. You can now use Reeder with an alternate service called Feedbin, or you can use it as a standalone RSS reader, just by punching in your feeds manually.
Unfortunately, Feedbin is a pay service (that costs US$2 a month to use), so it's not exactly a one-for-one replacement for GReader. But this is not the only update you'll see from Reeder: The company says the plan is to both update the iPad and Mac versions to 2.0 (which is why they're currently free), with plenty of extra compatibility, and the iPhone version is also set to get even more services in the future. So things are still in flux.
As for me, I still have to find a service to replace my GReader, and Feedbin isn't it. We've already put together a nice list of alternatives, and from what I've heard so far, Feedly appears to be the frontrunner. Feel free to share any other insight you might have in the comments below.