penders - 11:04 pm on Mar 4, 2010 (gmt 0)
To find out how many backlinks the search engines think your website has you need to perform a backlink search with each search engine. Google shares this information only with site owners when they log into Google's Webmaster Central.
I always thought google provided the publicly available link: instruction/prefix for this task. eg. link:www.example.com/index.html is supposed to return all the pages that link to this page. However, it never provides much in the way of results in my experience?! When Google's Webmaster Tools certainly does.
I suppose successful backlinks should appear in your referrer log?