On-Page SEO tools:
Google Keyword Planner
Anchor Text Over Optimization Tool
Copyscape
smallseotools
sitemap.xml generator
robots.txt generator
Google webmaster tool
Google Disavow tool
Google Analytics etc.
Off-Page SEO tools includes:
Majestic SEO
Ahrefs
SEOrush
Backlink watch
opensiteexplorer
Google Adwords etc.