http://ahrefs.com if my favorite site explorer at the moment. I haven't tried the paid version of it but can definitely vouch for the free one. It's still very powerful.

This post will answer most of your question..http://www.matthewwoodward.co.uk/exp...main-showdown/

Make sure you listen to the music !!

I’ve been using Majestic SEO and I find it as a reliable backlink checker. It has lots of features that I like including showing the websites linking to a certain website, the anchor text being used, and the page and domain authority of the linking page and site. Its Backlink History Tool enables you to know the number of detected backlinks for a certain domain, subdomain or URL.

I am mainly using free tools like "www.alexa.com" and backlinkwatch...

I use raventools

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backlink checker won't give you source from social media.
I believe the best tools is google webmaster tools where you can check most complete backlinks you get to your site by click on the "linktoyoursite".
You also can try of seospyglass and webceo, where you not only can check your site backlink and even competitors site backlinks as well.

In My opinion Ahrefs.com is one of the most reliable and prominent back links checker!

For me, backlinkwatch.com is good!