Google Plus does not offer RSS Feeds but you can easily generate feeds on your own using a new Chrome app developed by Eric Koleda, an engineer working with the Google Apps Script team. Here’s a sample Google+ Feed create using this tool.
To get started, launch Feed+ for Chrome and it will request access to some of your Google services. Say yes and you are all set to create RSS feeds from Google Plus. You can generate RSS feeds for individual profiles, business pages and for search results on Google Plus.
The generated RSS feeds are public and thus you, or anyone else, can subscribe to these feeds in any news reader. FeedBurner, for some reason, does not recognize these feeds as valid though I could easily subscribe to them in Google Reader.
And now that you have an RSS Feed for your Google Plus profile, you can easily cross-post updates to Twitter, Facebook, Tumblr, LinkedIn and everywhere else using the IFTTT service. You may also refer to my previous tutorial on how to publish RSS feeds to Twitter for more options.
If you are to ever disable a particular Google Plus feed, simple delete it from the Feed+ app inside Chrome. Also, you only need the Chrome app for managing the feeds - the Google Plus to RSS conversion happens in the cloud.
Google Plus APIs do not include details about Circles else it would have been more convenient to have a single RSS feed per Google+ circle rather than having to generate separate feeds for every member of a circle.
Also see: RSS Feeds for Google Search