Ahrefs: Ahrefs boasts the second biggest index of websites after Google. The tool is specially useful for SEO strategies and finding quality backilnks, including those for competitors. They offer a trial at $7 for 7 days.
Moz: Moz is one of the best know SEO tools out there. They are well known for creating the Domain Authority ranking system. A system that ranks websites on a 1-100 scale of their authority. Moz offer a 30 day free trial of their SEO platform.
Semrush: Semrush are another established SEO platform. They offer a free version with limited features, and paid versions. It's a popular tool with agencies. Features include daily rank change emails based on keywords.
Ubersuggest: This is a relatively new tool by Neil Patel. It has some free features and a reasonably priced paid version. Although, features and backlink indexing seem to be lacking in comparision to the other tools.
See this related article: 25 Best Free SEO Tools (2020)