Majestic Site Explorer
Majestic Site Explorer gives a generous amount of information for free, such as an overall trust index, and some backlink analysis including link types, depth, follow type, languages, and anchor text. Particularly usefully, It also charts your domain's backlink history for free so you can monitor how your efforts are proceeding.
If you verify your ownership of a domain, you gain access to extended information for free. Upgrading gives you deep analysis on referring domains, anchor text, and backlinks.