The only benefit I can see is to make a Facebook page (Google+, etc.) look more popular than it is. If I see a business whose Facebook page has only 45 likes then I'm not as likely to like them. But if they've got several thousand then I subconsciously think, "Hmmm...if this many people like them then they must put good stuff on their facebook page."
Just for fun I bought a thing on fiverr where someone promised to give me more likes by posting my page on their facebook fan page. They claimed to belong to a popular band with tens of thousands of fans. Well, the next day I got 16 extra likes all from people's whose names I couldn't pronounce. When I checked out those fans they were obviously fake accounts that were created just to boost like numbers.
Does it help SEO? No. I do believe that likes on a post can influence your seo. But Google is not dumb. If they see that I wrote a post that is getting hundreds of likes from around the world then they likely will promote my post a little more. But, I think they can tell if I'm getting hundreds of likes from paid sources. If I could look at the Facebook likes I got and automatically tell that they were spam accounts, I'm sure the algo can figure that out as well.
I personally don't think that having extra likes to your Facebook page is going to do anything for your SEO. But, if you have likes that are earned, then this indirectly helps. For example, when I publish an article on my site, I post it to my facebook page. If I have thousands of fans then that is a lot of people who can spread the word about my article.