Now that Google has broken integrated Google Reader with Google+, I was looking for a replacement that would let me use my daily reading of feeds the way I always had: as a way to share long-form content with other folks who specifically wanted to read the long-form content I shared this way (opt-in broadcast). Google+ defeats the purpose: I like my RSS feed and my friends' shared items specifically because of the high signal-to-noise ratio and the lack of dilution with other content.
My search led me to Tiny Tiny RSS. It offers a similar feature to Google's shared items, except instead of a specific social area it “publishes” items to your own RSS feed. It does not replace the comment or discussion capabilities of Google Reader, but it has the advantage of being something I can host myself and open source; if I ever have some free time I can address any flaws that continue to bother me.
It is not neatly packaged. You have to install the database schema yourself. You have to edit the config file by hand, including changing “ISCONFIGURED” to true at the end of the file. You need to set up a cron job to update the feeds (or a daemon, but they don't include any automatic launch capabilities if something goes wrong, or any logging so you'd be able to tell if it did. These are solve-able issues, but cron is fine for my purposes anyway.)
Despite these rough edges, it is very usable once you get it up and running. Importing my feeds from Google Reader took less than a minute. The UI is reasonably snappy. It does everything I need a web-based RSS reader to do and I haven't noticed features I greatly miss from Reader.
To get the RSS feed to share items with the world (including your friends still using Google Reader), under the Feeds tab of Preferences and the Published & shared articles and generated feeds section. Select Display URL and hand the resulting URL to anyone who wants to read your stream.
It may not replicate all the social features and it lacks the flexibility to share random webpages, but it lets me retain one of my favorite features of the old Google Reader while also giving me control over my content.