dear seo4ceo, To check the backlinks of your website: simply write this syntax in search engine: link:url (your site url) for example: link:www.mobile-phonesdeals.co.uk
Yahoo explorer is the goodway to check back links. Also webmaster and seoheap.com are nice tools, but they will list no follow links also.
Use open site explorer provided by SEOMOZ which has some advanced options like link authority and many.
You can check by type "link:http://www.yourwebsite.com" in Google or you can see links to your site in Google Webmaster Tools.