So, SEO changes all the time. I'd be writing every day of my life if I noted all the changes, as the algorithms will change multiple times in a day!
There are, however, some general rules that used to be in effect and now either don't matter or have fallen away through SEO changing, and some general rules to ensure you're doing or not doing if you truly care about rank. I have put together a list from several sources as sort of a cheat's snapshot guide to what SEO's current state of play is. Lots of valuable points came from an interesting thread that you should all spend some time in if you get the chance:
What is Important (i.e. pay attention to these)
As evil as Google is (for pushing it's own financial agenda), one of the most interesting new ranking signals is secure web pages. By pushing these best practices, Google ensures a safer searching environment for web users and knows the websites it refers to people are more likely to be as validly close to what it was the last time Google looked.
Quality site design
The last few years have ended up with us having bloated websites that look pretty but are terrible on load times, responsiveness and generally existing as a web entity. Quality is more than how pretty your site is, it includes things like UI, UX, technical prowess, user flow and general efficiency.
Focus on all the elements that affect user experience, like page load speed, what renders and when, nav etc.
This is a no-brainer that has been harped over and over for several years, and is still prevalent. Keep your content original and unique, write engaging content that provides an answer to the searcher's question, teaches the visitor, informs or gives broader information, and is useful, and you will improve your visibility.
While this isn't a huge one right at the moment, this will become more important as time goes on and as Google cares more about absolutely unique content.
Shorter title tags
Titles have become so bloated over the years because we used to try to capture people's attention with the biggest text possible. Keep it short and on-point and your content will naturally rank better.
Descriptive meta description
This is important because there are still so many sites missing core meta descriptions and while it does not affect rankings, it does affect your CTR (Click Through Rate) from Google.
Be natural and don't stuff
Implement the keywords you would like to use in a natural manner. Stuffing is a big no-no and has been touted for ages, so stick to not stuffing!
Remember the basics
The core elements like your H1, H2 and title tags should not be forgotten and definitely still matter.
What's Not Important (i.e. if you're doing these, you're wasting your time)
These haven't mattered for a while now and while some say it's good from a clean-code perspective, it doesn't bring any SEO value.
Too much focus on long-tail phrases
Because Google is getting smarter at recognising what we mean with lots of signals coming into play in that decision, longtail keywords are now not as important as they used to be.
Content for content's sake
Writing content for the sake of content creation is no longer a signal of a fresh site or a resource that's valuable, instead the content needs to be valuable.
Excessive number of pages
It used to be common practice to exhibit the size (and thus 'value' of your site by having inventory/CMS systems spit out these relatively 'thin' pages for the sake of having a page that could be referenced. This is no longer useful and actually goes against you in the sense of when Google looks at pages for usefulness.
As you can see, there are various things that a few years ago used to matter a lot, and some things that we hadn't even considered back then which are important now. Apart from keeping up with how things are changing, it's always good to explore other SEO's opinions of what they've found matters. After all, we are all looking at what Google does and have unique takes on their approach, so while it's time intensive, do try to spend some time exploring what reputable people have to say if you have the interest!