The most popular way to do this is using Yahoo Site explorer.  And it is free.

http://siteexplorer.search.yahoo.com/

Why do you need to know about the number of backlinks to your site?  Backlinks are still a major part of Googles algorithm despite updates like “panda” that have penalized some sites with significant numbers of back links.  The sites that have been penalized are ones that do not have frequent good quality content.  Or sites that have added their backlinks too fast.

If you do start a backlink campaign be advised that new SEO backlinks may take a few weeks to show up on the Yahoo backlink checker tool.

For a safe and reliable backlink service you could try BuySEOLinks.net

SEO backlinks are a very important way of getting traffic to your site by using SEO to improve your rankings and therefore getting free search engine traffic.  This means you will get  a steady flow of traffic to your site without paying for it.