There are only a couple of weeks left until Google Reader shuts down. Like many other people (the "loyal but declining" following the product had certainly numbered in the millions) I've been looking at alternatives for a while now. I've finally settled on feedly.
Feedly isn't quite a drop-in replacement for Reader, but it's the closest I've seen so far for someone in my position, which is to say a Mac/Safari + iOS user. They also claim to support Android, Firefox and Chrome but I haven't tried it with those yet, and if you're primarily Windows or Windows Phone then you may need to look elsewhere.
The reason feedly is so close to being a direct replacement for me is that they are concentrating on being an API level clone of Reader, which means they can bring the iOS application developers with them. I've used Reeder as my Google Reader interface on the iPad since it came out, and the developer is planning feedly support. For now, I'm using feedly's own iOS application. This does fall over occasionally while running on my memory-constrained first generation iPad, but otherwise seems fairly solid. If the reliability improves by the time the new version of Reeder is available, I may stick with it; as Reeder will require iOS 6 I'd need a new iPad anyway.
My final concern is that the feedly service is free, but already supporting something over seven million Reader refugees. I really hope they find a decent way to make this pay.
[Updated 2013-06-19: removed paragraph mentioning that there was no conventional web application, because there now is one.]