Free SEO Tools

http://www.removeem.com/ratios.php

Link Research, Technical SEO

Worried about Google’s Penguin algorithm hitting you for over-optimized anchor text? Simply type in your URL for a full report of which links might raise flags.

http://www.bing.com/toolbox/webmaster

Tools Suite, Diagnostic

Similar in function to Google Webmaster Tools, Bing offers a suite of interesting research tools and resources for webmasters

https://moz.com/tools/seo-toolbar

Tools Suite, Toolbar, Moz

The standard SEO toolbar for legions of marketers, the MozBar allows you to perform over 50 key tasks right from your browser. Highly recommended.

http://www.socialmention.com/

Social

Social mention offers real-time social media search and analysis. Enter a search term and see who’s sharing what, right now

http://www.seoquake.com/

Toolbar, Tools Suite, Technical SEO

SEOQuake software tool will show you the rankings for your competitors and yours as your sites as you search then internet.

http://www.virante.org/seo-tools

Tools Suite

Virant offers a number of high quality SEO tools to the public. These are often the same tools developed for the Virant team, opened up for public use.

http://domainhunterplus.com/

Link Building

This magic extension for Chrome not only helps you find important broken links, but also tells you if the links point to an available domain.

http://www.google.com/analytics/

Analytics
The most popular of all the analytics tools available, Google Analytics continually innovates and sets the standard.

http://www.google.com/mapmaker

Local
Among other things, Google Map Maker allows you to contribute to public map information, which may be shared and incorporated into Google Maps.

http://www.internetmarketingninjas.com/tools/

Tools Suite
The Ninjas are some of the best SEOs and online marketers out there, and they’ve put some of their best tools online for free.

http://www.barracuda-digital.co.uk/panguin-tool/

Analytics
This awesome tool connects with your Google Analytics account to help you see if and when you’ve been hit by Google Algorithm update

http://tools.seobook.com/firefox/rank-checker/

Rank Tracking
This light and easy desktop tool checks rankings with the click of a button. Quick, easy and free.

https://ahrefs.com/

Link Research, Link Building
One of the more popular link research tools, Ahrefs offers a large index and nice anchor text distribution charts. Mostly a paid tool, but they offer some free data.

http://www.majesticseo.com/

Link Research, Competitive Intelligence, Link Building
You’ve probably seen Majestic SEO link charts all over the Internet. Great crawling technology combined with several free options make for great link research

http://www.wordtracker.com/
Keyword Research

http://www.semrush.com

A powerful keyword research suite used by many top marketers, Wordtracker offers a generous free trial option.
Find hidden Keywords for your niche as well as your competitors keywords