Everybody has their own opinions of what works and what doesn't work, and SEO in itself can be highly subjective, primarily because Google doesn't really come out and specifically admit the things that work, because they don't want people gaming the system.
Moz published a blog post "Amazing Correlation Between Google +1s and Higher Search Rankings" claiming that Google +1s had a direct correlation with higher search rankings in Google – and that it was higher than any other ranking factor. The post was written by Cyrus Shepard, the "Senior Content Astronaut" at Moz, and the data was taken from their 2013 ranking factors.
It's a pretty sensational title, and immediately sparked a lot of discussion. His post brought up a lot of points about why he feels this correlation is correct, such as posts shared on Google+ are crawled and indexed almost immediately, and that posts on the site pass "link equity". He also noted that authorship shares in the rankings as well. However, he's also stating it as fact, instead of just a possibility without any specific hard data with proof, such as specific sites where an increase in rankings can be solely attributed to Google +1's.
In addition to grabbing the attention of many in the SEO industry (many of whom trashed the post as being highly flawed), Cutts immediately stepped into debunk the claim of the correlation between rankings and +1s. Specifically, Cutts wrote:
Just trying to decide the politest way to debunk the idea that more Google +1s lead to higher Google web rankings. Let's start with correlation != causation: http://xkcd.com/552/ But it would probably be better to point to this 2011 post (also from SEOMoz/Moz) from two years ago in which a similar claim was made about Facebook shares: http://moz.com/blog/does-google-use-facebook-shares-to-influ... . From that blog post from two years ago: "One of the most interesting findings from our 2011 Ranking Factors analysis was the high correlation between Facebook shares and Google US search position."
This all came to a head at the SMX Advanced search conference in 2011 where Rand Fishkin presented his claims. I did a polite debunk of the idea that Google used Facebook shares in our web ranking at the conference, leading to this section in the 2011 blog post: "Rand pointed out that Google does have some access to Facebook data overall and set up a small-scale test to determine if Google would index content that was solely shared on Facebook. To date, that page has not been indexed, despite having quite a few shares (64 according to the OpenGraph)."
If you make compelling content, people will link to it, like it, share it on Facebook, +1 it, etc. But that doesn't mean that Google is using those signals in our ranking.
Rather than chasing +1s of content, your time is much better spent making great content.
So his belief falls in line with what a lot of SEO professionals are doing for long-term SEO success, where creating great quality content that is more likely to be shared is the best kind of strategy when it comes to content.
He does continue to reiterate that +1s and rankings are not related. "Most of the initial discussion on this thread seemed to take from the blog post the idea that more Google +1s led to higher web ranking. I wanted to preemptively tackle that perception."
Cutts also mentioned that another SEO has been doing a rigorous study on whether it +1s lead to higher rankings are not, which he suspects will be released the next month or two. If it is providing specific examples in the study, it will be good to be the most conclusive evidence SEOs will have about whether it is or isn't a ranking factor with concrete data to back it up.
Cutts made similar statements last year at SES San Francisco, when he said that Google doesn't put a lot of weight on +1's yet and advised people not to assume Google+ equates to rankings.