General site health and compliance
W3 Validator
Markup validation service.
Google's Structured Data Testing Tool
Structured data testing tool. If you have structured data related to your business location, reviews, recipes, etc. you can use this tool to check source code or an existing page to validate its structured data.
Google's PageSpeed Insights
Page speed testing tool. If your site is slow on a desktop or a mobile device, Google will not appreciate it. Get feedback on individual pages and suggestions to improve performance.
Pingdom
Get advanced information from aggregate and individual user sessions to see where the bottlenecks are in your site’s performance.
Browseo
This site allows you to see your pages like the search engines do. This is very helpful to make sure all of your content is readable and crawlable.
Xenu's Link Sleuth
This software program will allow you to crawl your site, find broken links, and create a valid xml sitemap.
Google Mobile-Friendly Test
Google wants your site to be mobile friendly as more and more users see the web on their mobile devices. Google’s tool gives you the thumbs up or thumbs down as to whether or not they view a page as mobile friendly.
Google Webmaster Tools
A full suite of feedback from Google in regards to how your site is being indexed, where you’re ranking in keyword searches, crawl errors and more.
Bing Webmaster Tools
Bing’s similar version to Google’s Webmaster Tools, offering similar information from their perspective.