HTML Validator (W3C)

Also known as the HTML validator, it helps check Web documents in formats like HTML and XHTML, SVG or MathML.
CSS Validator (W3C)

Validates CSS stylesheets or documents using CSS stylesheets. In addition to validating your CSS, it also warns of possible usability problems.
http://jigsaw.w3.org/css-validator/
MobileOK checker (W3C)

This checker performs various tests on a Web Page to determine its level of mobile-friendliness.
Link Check (W3C)

Checks anchors (hyperlinks) in a HTML/XHTML document. Useful to find broken links, etc.
http://validator.w3.org/checklink/
RDF Validator (W3C)

Checks and Visualize RDF documents. The RDF Validator parses your RDF document, checks your syntax, and generates tabular view of your RDF document.
http://www.w3.org/RDF/Validator/
Feed Validator (W3C)

This is the W3C Feed Validation Service, a free service that checks the syntax of Atom or RSS (Really Simple Syndication) feeds.
Website Performance Test

Pagetest is an open source tool for measuring and analyzing web page performance right from your web browser.
http://www.webpagetest.org/test
Accessibility Evaluator

WAVE is a free web accessibility evaluation tool provided by WebAIM. It is used to aid humans in the web accessibility evaluation process.
All-in-one Website Analysis Tool

Find out how well your site is doing in popular search engines, social bookmarking and other site statistics.