Moz.com (formerly seomoz.com) is one of the most popular SEO services due their useful tutorials for website owners and SEO specialists. Recently, since Google has dropped the support for Page Rank (PR), 2 metrics created by Moz have become very popular: DA (domain authority) and PA (page authority) and are used by the SEO world as a scale to measure the reputation and the "link power" of a website.
Moz.com offers a free trial and they have an useful browser add-on/toolbar to display DA/PA of a website or for search results.
It shows local and global search volume, also the keyword difficulty.
It displays DA/PA, you can filter links by follow/dofollow, only external/internal, group by subdomain and more.
Moz is i great resource of information for SEO beginners and advanced ones. Their blog and forum provide really useful information, always updated. Regarding the tools, Majestic and Ahrefs are reporting more valid links than Moz. Otherwise you will find some useful tools in there.