Google Reader was merely the most popular 'client' app - its disappearance wouldn't spell the doom of feeds (RSS/atom/whatever), and here's why: practically all the major publishing apps have RSS functionality built-in.
Do you use Wordpress? You probably have an RSS feed whether you're aware of it or not.
Using phpBB? You probably have an RSS feed.
Started a subreddit? It comes with a bunch of feeds.
facebook still offers an RSS for timelines, but you'll have to get it first as it's keyed.
twitter doesn't offer an RSS at all, you'll just have to use the APIs (and you'll need to authenticate even if you only want public read access, so you'll have to register, too). And don't think about trying to offer an API-to-RSS bridge, Twitter doesn't take kindly to such awesomeness; http://tweet-2-rss.appspot.com...
These 'social media' platforms of course want you to stay inside their boundaries. If you want to know what @Whoever is up to, you'll just have to view twitter or, better yet, 'Follow' that user and make sure you've got yourself logged in on as many devices as possible preferably with the official twitter apps.
So what happens when a company no longer regularly posts their news or blog posts via their regular content delivery, and instead takes to twitter / facebook? The feed dies out. Sure, it's still there, and maybe once in a blue moon some new content does pop up on there.. but for that same content and everything else you'd be interested in, you'll just have to check them out on facebook and/or twitter.
It's only when companies start realizing this shift - and, again, they might not even be fully aware that they're offering a feed in the first place - that they might try shutting it down for fear of not reaching the right viewership (in the way they want, including the possibility of deleting a post that they later regret).
At least feeds will remain as the premiere way to deliver podcasts (hacked on as they are)