1.1. Google Images: reverse lookup an image to find if an image or graphic you created has been used without attribution, then reach out to ask for a link.
1.2. Google Alerts: Get alerts when a keyword is mentioned in content. Google for citation link building.
2. Technical SEO
2.1. SEOTools for Excel: Suite of tools, including pulling meta title, meta description of URL, checking HTTP status codes of URLs and more. A personal favorite.
2.2. Screenfly: test your website on different devices and resolutions
2.3. Ayima redirect path chrome extension: shows redirect path of any given URL
2.4. Google Webmaster blog: not a tool, but contains the answers to some of the most difficult technical SEO questions
3. Keyword & competitive research
3.1. UberSuggest: long tail keyword research. Keywords often don't show up in Google's keyword planner.
3.2. Word Frequency Counter: good for competitive/keyword research
3.3. Wayback Machine: check old or deleted pages on any website. Comes in hand for competitive research
3.4. Builtwith: find out what websites are built with (CMS, etc.)
4. Content
4.1. APIs Dashboard: all of the most popular APIs on the web
