Long before Google Reader announced they were shutting down, I chose Fever, a self-hosted solution. You pay once for a license, install it on your own LAMP server, and upload your OPML file or just add feeds as you need to. The developer, Shaun Inman, pushes updates as needed, although Fever is not really his priority now, as he's working on game development.
The stand-out feature of Fever is that it algorithmically combs your feeds for "hot" stories, presumably by looking at hyperlinks that are included in many feed items over the same period of time. This allows me to quickly see what's hot among the blogs that I visit. In addition to being able to click on the story that many blogs link to, I can also peruse all the posts that write about the story.
Fever works in the browser, and although it is optimized for the iPhone, there are also two iOS apps that use the Fever API to improve the reading experience as well as allow you to download posts for reading when you're, say, on the subway: Ashes and Sunstroke. I'm not going to provide a review here of both apps. I'm partial to Sunstroke, but I haven't been following recent updates to the Ashes app.
Although I am intrigued by Dave Winer's River of News, I do value the ability to download feeds to my iOS device - having a browser-only reader doesn't suffice for me. (Recently, instead of using a Fever app for the subway, I've just been combing Twitter during breakfast, saving lots of links to Instapaper, and reading the articles in the Instapaper app on the subway. Sometimes I just feel that syncing all my Fever "kindling" posts to my iPad takes too long, or the app "times out.")
I also have FOMO ("fear of missing out") with regards to certain feeds. Like, I want to read everything from certain blogs, and if the authors of these blogs don't post frequently, I may miss their posts in a big River of News. (Of course, I could just visit the blog.) But at least with Fever, I can have a group of favorite blogs, and Fever doesn't "mark all as read" unless I want it to.