As the question is WordPress specific my list is mostly WordPress plugins.
404 to Start
This plugin eliminates 404 errors when someone attempts to access a page that no longer exists (or never did). Excessive 404 errors are reported to have a negative impact on your sites search ranking. It’s easy to configure this plugin so any time someone accesses a non existent URL what is returned is the home page of the website.
The user will never get what they’re looking for (as the URL is non existent) but at last you eliminate the 404 errors.
Broken Link Checker
Generates a report of any broken links on your site (links that link to non existent URLs) so you can easily find them and fix them.
A commercial plugin that gives someone a link when they leave a comment.
Contextual Related Posts
The titles (and only the titles) of five similar posts are displayed on the webpage of every post. This causes your important keyword phrases to appear more often on the webpage without you having to keyword stuff the post.
Evergreen Post Tweeter
While the link from a single tweet provides very little Google link love, it does provide a little. This plugin allows you to randomly grab blog posts and tweet them out to the specific twitter handle at specified intervals. I recommend using the twitter handle of the business rather than a twitter handle belonging to any individual.
EWWW Image Optimizer
Small images load faster. Page load speed is an SEO factor. Faster load times helps with site ranking.
Google XML Sitemaps
To make it easier for Google to find EVERYTHING on your site, you need a sitemap.xml file that is updated every time your website is updated. When you publish a new blog post, your sitemap.xml file is updated. This plugin does that.
Greg’s High Performance SEO
This is my preferred SEO plugin. It’s highly configurable and if you’re brand new to WordPress and SEO I recommend a simpler one, but his is the one I prefer.
Hide YouTube Related Videos
If you embed YouTube videos into your blog posts, this prevents the display of related videos when the video you’ve embedded ends. This is not so much an SEO thing as I consider the related videos feature of YouTube to fine for videos on YouTube, but when that video is displayed on my website I want it turned off.
A plugin from HubSpot that captures details every time someone fills out a form on the website. Those details are then sent to me via email.
Not an SEO plugin per se, but makes it easy to create visually obvious Call to Action buttons.
Smart Google Analytics Code
Also not an SEO plugin per se, but makes it easy to install the Google Analytics tracking code onto your WordPress website as well to verify your website to Google Search Console.
That’s Actually 9 + 3
Nine of the plugins listed provide a direct SEO benefit. For the other 3 the benefit is either indirect or something other than SEO.
Learn More…SEO Needs Link Building