A lot of good answers above but as times change so to do the ranking signals used by Google. Some signals gets devalued, other signals increase, and still others are either added or removed.
Here is a list from November 2016 which has been compiled through SEO sources, Google information, etc. Some have been proven, some are controversial, and others are speculation...
Domain Name
Confirmed
Google's Matt Cutts has gone public implying that domain age, while not a very important signal, is used by Google to some extent.
http://www.youtube.com/watch?v=-pnpg00FWJY&feature=player_embedded
Top Level Domain Keyword Appearence
Unverified
This doesn't give as much of a boost as it used to however having your sites main keyword in the domain name can still act as a relevancy signal to some extent. This is further reinforced by the fact that Google still applies bold type to keywords that appear in the domain name.
Keyword As First Word In Domain
Unverified
A domain that starts out with its main keyword can rank higher that sites that either don't have their main keyword in the domain or have it in the middle or end of the domain. As with the above point 2 it doesn't provide as much of a boost as it once did but it can still be considered a relevancy signal, especially when taken with other relevancy signals.
Domain Registration Length
Implied / Controverstial
Google registered a patent back in 2005 for "Information Retrieval Based on Historical Data". In the patent Google reports that the registration date of the domain can be of use in ranking as an older domain is more likely to be of value and a legitimate domain as opposed to a more recently registered domain. At the same time in the patent Google reports that valuable (legitimate) domains are often paid for several years in advance while doorway (illegitimate) domains rarely are registered for more than one year and so the date when a domain expires in the future can be used as a factor in predicting the legitimacy of a domain and so the pages within the domain. This argument is contested hotly amongst SEO sites, including the Search Engine Journal, who released an article in July 2008 stating that domain age is both an overestimated and a misinterpretedt signal and that the domain registration date cannot speak for either the quality or trustworthiness of a website as domains can be parked for a long time, established companies can change domain names and 301 redirect the old domains pages to the new domains pages, and more importantly a domain name can be used illegitimately for years but then be sold to a legitimate person or company without any change to the registration date. We see this more and more with companies who make their business models on mass registering domain names and then selling them to customers at a premium. The registration date generally stays the same and ownership of the domain merely passes to the new owner.
Keyword in Sub Domain Name
Unverified
In 2011 Moz's panel agreed that keywords appearing in the subdomain can boost rankings. The degree to which this boost helps, or even the fact that this boost exists to begin with is contested in many circles and has not been able to be verified in the past.
Domain History
Unverified
There are some corners of the SEO sphere where the claim is made that volatile ownership or several drops on a domains whois record may signal to Google to "reset" the sites history which could have the effect of negating links which already point to the domain. To date this has not been verified by Google.
Exact Domain Match
Verified / Removed
For a while a domain could rank in the top 3 even with no backlinks by having an exact match domain (EMD or Keyword Domain). The way this worked was that if you wanted to rank with the term Aussie Bearings an exact domain match would be aussiebearings.com. That signal however has been removed since Google's EMD Update made in 2012 which closed the loophole.
Public vs. Private Whois Data
Verified
It is believed that private Whois data may be a sign of "something to hide". Google's Matt Cutts is quoted in 2006 as saying that when he checked on a number of flagged sites they all had whois privacy protection services which he considered to be unusual, but that it isn't automatically bad and once several factors are together then you may be talking about a different situation. What this seems to indicate is that while Whois data being protected is considered it is a very low ranking signal and is more to do with the manual action process as opposed to any automated ranking process though this is an educated guess based on the quote from Matt Cutts.
https://www.searchenginejournal.com/seo-question-do-whois-privacy-services-harm-seo/5874/
Penalized Whois Owner
Unverified
Similar to point 8 it makes sense that if Google identifies a domain owner who has violated the terms on one site there is a reasonable chance that it may be happening on other sites and so those other domains may need extra scrutiny. Once again though it is unlikely that this signal is used in automatic ranking and more likely that it is used to identify sites needing further review.
Country TLD Extensions
Verified
Having a country code top level domain (such as .cn, .au, .uk, .ca, etc) is a signal that can help a site rank for a particular country but it does then limit the sites ability to rank globally for a global Google search or on other country coded Google searches.
Keyword in Title Tag
Verified
The title tag is the second most important piece of content for a given page beside the page content itself and so send a very strong signal.
Title Tag Starts With Keyword
Verified
According to Moz Data title tags that start with a keyword tend to perform better that title tags with the keyword towards the end of the tag. It should be pointed out though that this doesn't take into account other signal which may have affected the ranking and is at best an educated assessment based on a blind study without access to the Google algorithm.
Keyword in Description Tag
Verified
Adding keywords to the description tag provides a low ranking relevancy signal. Google does not count description tags as a high value signal due to the potential for misuse but it can still be used to pass some limited relevancy signal.
Keyword Appears in H1 Tag
Verified
If you have a keyword appear in a H1 tag (which is generally considered like a second title tag) then it can send another relevancy signal to Google. The importance of the signal is unknown but the fact that it is a signal that Google takes into consideration is known.
Keyword Frequency In Document
Verified / Reduced Importance
At one point a page could rank very highly by repeating the same keywords all over the page in order for the frequency of that keyword to go up and make it an important signal. Due to the potential (and historical) abuse of this signal it has been reduced and a focus has been placed more on the natural appearance of keywords in the page rather than forcing ways for keywords to appear.
Content Length
Verified
While it is known that content length plays a part in ranking recent studies have found that shorter high quality pages can often rank higher than longer but lower quality pages. What can be taken from this is that quality over quantity is more important now and this signal has reduced significantly and may in fact be removed in the future given Google's improvements to indexing and analysing the natural language of the page content.
Keyword Density
Verified
While not as important of a signal as it once was due to misuse and abuse keyword density is still used to some extent by Google to determine the topic of a page, however excessive keyword density (also known as keyword stuffing) can have the opposite effect and actually reduce your ranking.
Page Loading Speeds
Verified
Page loading speeds are used by all of the top search engines on the web as a ranking signal. Some do this based on HTML and estimating the load speed based on the size of the HTML content delivered itself, others (like Google) monitor the actual metric of page loading by testing it with crawlers designed to emulate the browser downloading and rendering the page to get a more accurate page load speed.
Duplicate Content
Verified
This signal is a very high ranking signal used to reduce your sites ranking as opposed to increasing it. If duplicate content is detected (even if it has been slightly modified) it will cause the ranking for the page and potentially the whole site to go down substantially.
Rel=Canonical Tags
Verified
This signal is not used so much to improve ranking as it is to reduce the chance of being penalised by the duplicate content signal. This tag denotes that the page is in fact a duplicate and tells Google where the actual page is. In many instances any ranking that is attributed to the duplicated page will be applied to the canonical page instead.
Recency of Content Updates
Verified
Ever since the Google Caffeine update Google has ranked recently updated content (and more frequently updated content) higher than older content. On many occasions Google will add a date to the results listing to show that it is a recently updated page and the date that it was updated, especially for time-sensitive searches.
Keywords in URL
Verified
Having keywords in your URL is an important relevancy signal and should be done where possible.
There are a great many more and I could spend the next 6 hours going through them all however the basics are quality over quantity, and design your site and content for your users and not the search engine. As long as you follow these rules you should be by and large hitting all the important signals.