Be careful not to paint with such a broad brush. Many webmasters miss the finer details that make a big difference.

For example I would not simply list Links / citations as a signal. That is too broad, here are some finer details for links:
-anchor text
-nofollow vs dofollow
-relevancy of linking page
-age of link
-placement of link on page

I would also suggest that webmasters be careful not to look at this list of signals as way to shortcut the system. It is often easier and more profitable to build a legitimate site which can naturally generate these quality signals than to falsely generate them for a spam site (though it is still possible to make money from spamming the Google serps if you know what you are doing).

To be honest I am not 100% sure about every specific factors that Google is currently using. I have noticed that websites that get a strong boost in social marketing (twitter, facebook, google+, etc.) tend to get a ranking boost.

Is this because Google is tracking tweets or facebook likes? I have doubts that Google is directly doing this since Facebook really does not like Google and would likely try to hamper Google. So maybe this is because Google pays attention to data gathered from Chrome users and could thus identify successful social campaigns. Possibly or maybe this is because that a successful social campaign leads to more brand awareness and thus more people typing your brand name into Google's search box.

It is very hard, if not impossible to completely isolate and identify the specific signals that directly drive rankings. It is much easier to identify signals that have a strong correlation to rankings whether through direct influence, indirect influence or just coincidence.

The value of citations is a curious one for me. One possibility is that citations have no inherent value of their own. Perhaps the value is that a non-linked citation causes some amount of searches for the domain name and/or direct traffic via cut and paste.

That's assuming that searches for brand/domain and direct traffic (detected via Chrome?) are signals themselves.

I have noticed that websites that get a strong boost in social marketing (twitter, facebook, google+, etc.) tend to get a ranking boost.

There are certainly ways that people use to rank websites without using keywords and links, but so far, they don't work in Google that much, including Social Media.
I think you are misinterpreting Google search results.
My model for Google is this. Their search results must favor big brand-name sites because big brand-name sites run Google ads. To do otherwise using Social Media to rank websites and professionals/influencers would be to sacrifice too much revenue, they would be going back to pre-Adsense when all of their income came from ads right on the search engine page.

Your brand name

I've heard this "“Google Search Engine takes a direction to becoming a Reputation Management Search Engine.”
If they decide it works for advertising they might try it to the extent it won’t jeopardize their earning, but my guess is it would work badly for advertising, because people with real reputations to manage aren't interested in having ads run against their online work. Just think about what appears in the ads for searches on medical terms, for example, and you’ll understand why no medical professional would want his article about infertility sandwiched in Google ads, same for cancer doctors, etc. Same for scientists. same for teachers, same for everybody who comes to mind.

Quality

“So, why do many sites out there still care about their social media presence and their content quality?”
The successful how-to/information sites tend to be crap, though they are slightly better crap than a few years ago because they use their Adsense earnings to pay for editing (and promote their brand in social media). You will never find competent professionals to write Internet pages in their field for a price that makes it work for the website. As the biggest sites get bigger, they do trend to better quality because they have the Adsense to pay for it and the fear of Google changes to drive them, but it's not quality that got them to the top and more importantly, it's not quality that will keep them there.
It's pleasing Google, which is SEO, not content.

A few more "known" factors:

what results people click on, how often people hit "next page," how humans rate the results before and after [an algorithm change is tested]

These are examples of data that is being used by Google, provided by someone who works for Google.

[webmasterworld.com ]

how humans rate the results before and after

Yea. Stay-at-home moms being paid to evaluate websites on subjects they have no interest in are left judging 100% on appearance. They will always pick the medical advice site that has an illustration of a pretty white baby or a dignified doctor over a site with no pictures. Yes, Google wants to present websites (with ads) that people will trust, but trust doesn't equal quality, the two have nothing in common.

I do believe that Google+ mentions/button clicks play a SIGNIFICANT role in rankings. Unlike the FB likes, Googlebot can clearly see these.

There has already been backlash against artificially boosting G+ prominence, but I do think that it helps.

I think you are misinterpreting Google search results.

I am not interpreting the Google search results, I am making an observation that has been mentioned by others who have done much more formalized research and also found a correlation between social signals and rankings. In case I was not clear, I was using that observation to make the point that correlation is not causation and that it is very hard to isolate and identify the specific direct influences on rankings.

Let's also be careful to not waste time complaining about Google since complaining does not help any of us to increase our website profits.

Now let's get back to the main focus - What signals count for Google rankings whether directly, indirectly or just have a high coincidental correlation?

I think a very generalised "what works for Google" is a website that could survive without Google traffic, i.e. it has a presence outwith a strong backlink profile that could have naturally or unnaturally been acquired.

- Social mentions would validate this, but reinforced by knowing who does the mentioning and their position in the network of people (has 1 friend or lots of friends, friends with authorities etc)
- Relatively (relative to other sites ranking in the same query) low bounce rate
- Links from authorities relating to the query
- Traffic arriving via areas that Google tracks (their DNS service serves hundreds of billions of requests a day, whose domains are getting resolved?)
- Non-link citations

Again, very generalised, I'd say 'link juice' is still very important but it gets validated by the way people interact with your site, and whether you're being mentioned outside of links.

Two that some have thought to have been ranking factors, but stated later by Matt Cutts as specifically NOT having an effect:

- WC3 Compliant and/or Broken HTML

"Matt Cutts said, “so Google does not penalize you if you have invalid HTML, because there would be a huge number of web pages like that.”

- Google +1 Widget

"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" - Matt Cutts

I had some success promoting someone for strategic reasons with a very common name, utilising YouTube which in itself attracted a lot of attention. All other sites with their name surfaced, attributable to that person as a consequence.

There may be some lessons out of that as part of how brand signals can play in. ie Google knows you saw a brand on YouTube , then assumes by your history and/or popularity a set of predictive results in the SERP's and of course populates Google suggest.

Two words: Bounce rate.

I have more than enough data to support that statement.

Bounce rate does make the most sense. It is the clearest signal to google that you are providing the content that the searcher is looking for.

@Andem

Two words: Bounce rate.

I have more than enough data to support that statement.

Is that "bouncing back to the SERPS" or the general bounce rate, like you would see in Google Analytics? I have some sites with a high GA bounce rate that do just fine in ranking. The high bounce rate seems related to clicking on an ad and following on to a different website, vs back to the serps.

Bounce rate does make the most sense. It is the clearest signal to google that you are providing the content that the searcher is looking for.

So, does it mean the searcher left because the site sucked meaning the search engine missed the mark, or does it mean the searcher found the right answer on the first page they visited meaning the search engine was right on with the result?

I'm not sure how bounce rate is a "clear signal" by any means in isolation, but it could be I'm missing something by trying to take into account both sides of what it would possibly mean and how, as a search engine, I would interpret that.

The high bounce rate seems related to clicking on an ad and following on to a different website, vs back to the serps.

It's been said [by JohnMu, I think], even when people find "the answer" on a site they tend to "bounce back to the SERPs and continue clicking on results or refining the query" more often than not. Why? I'm not sure, possibly simply because it's "search", possibly for verification from another source, or possibly for more detailed information about a topic, but, whatever the reason, it still seems like it's a noisy signal to me, which has been stated repeatedly over the years by Google reps. for some reason.