SEO Quack for check keyword density, site audit, alexa ranking and many more. use google keyword planner tool for keyword selection. google analytics for traffic and google webmaster for website proformance. many more tools
MOZ bcoz by which I can generate a report on a website showing which pages are ranking for which keywords, which are close to page 1, how they could be refocused to hit page 1 etc. For on-page/on-site SEO I think it's very valuable.
The Tools using for doing Search Engine Optimization are:
Google Analytics
Google Webmastertool
Alexa.com(Monitoring Traffic)
SE rankings(Track Rankings)
Ontolo( For Content Marketing)