I thought this article was interesting:
Facebook Likes, Shares Don't Impact Google Search Rankings [Study] (searchenginewatch.com)
After creating two different web pages on three different domains, he had friends and Fiverr users drive likes to each of the pages. Despite each of those pages being liked nearly 900 times each, Google never crawled are indexed any of the six pages. So Google clearly is not using Facebook likes to discover or index new content.
And then with Facebook sharing, the data was inconclusive whether or not they matter or not.
The article goes on...
While there's no clear-cut evidence whether Google is or isn't doing this, the opportunity is there, which also means that it is potentially beneficial for users to be friends with high profile users, and those with strong profile pages in Facebook.
One interesting thing was that Enge also discovered that Google has indexed a large number of Facebook posts – 1.87 billion to be exact. So next they looked at those with high PageRank profile pages, from people linking to their profile page, to determine the frequency that those higher authority users saw their post content indexed. However, while the results showed that some of their posts were being indexed, the percentage of content indexed from the profile page was in the neighborhood of 60 to 70 percent, depending on the age of the post.
They're saying that just because Google isn't doing it now doesn't mean they can't or wont in the future. They could start using this data at any time.
Getting likes on a page or sharing a page definitely has value, so don't stop doing it. If people come to a page and see the Facebook widget at the top with a good amount of likes or shares, that says something about the content there. Remember, social media is social. There's that social element. If other people like it or share it, maybe you will like it, too. Also, when people share your website's content, it's showing up on other people's news feeds and that gets you more traffic. Facebook is where people are and you want to be in front of people, so by no means stop utilizing Facebook just because Google doesn't seem to use it right now.
We tell clients to not set up a corporate/organization/business Facebook or Twitter account unless they're going to actually get into them and use them. It's social. If you're just going to be in the room representing your company and not say anything or not respond when people try to talk to you, then it's better that you don't even show up to the party. It'll be better for your reputation for sure.
Probably the best way to start using social media like Facebook is to get a younger person who works at your company trained on how to use Facebook for business. They already know how to use it and they can be trained on company policies and what you do and do not want posted on the company page. They can also reach out to the circle of friends they already have and start to make more connections. Get them trained on what kinds of posts to make, what to say and when the best times are to post - they'll love it.
Again, don't stop using Facebook but just know that right now it's not going to affect your website's rank on Google. In other words, if you're posting mindless things thinking that Google is paying attention, then stop that. Concentrate on real posts on Facebook that matter and that grow your community and influence there.
[Update - 01/28/14:] I found another article that came out that relates to this topic:
Matt Cutts: Facebook, Twitter Social Signals Not Part of Google Search Ranking Algorithms (searchenginewatch.com)
Google doesn't seem to be using Facebook and Twitter social signals when it comes to ranking. However, there are obviously still plenty of benefits and marketers shouldn't cease those benefits simply because there doesn't seem to be direct relation between those two social media platforms and Google ranking.
They're saying no again here still but also say that it could change. The traffic is over on Facebook and you want to be in front of traffic. If your business or organization works with a Facebook audience and if you can put in adequate time to work with that fanbase, then there still doesn't seem to be any harm in doing Facebook marketing - only positive things.