Have you looked at Traffic Travis? It has a free version that can help you check backlinks as well as do keyword research and on-page SEO analysis for you. Hope that helps. Have a good day!
SEO is the best way of link building but don't just make backlinks randomly. Try to build quality and relevant backlinks which is more worthy for your site.
There are many tools to check backlinks namely Backlink watch, link diagnosis, iweb tool, open site explorer... You can easily get it from google because i just googled then only i got more results
Check out Ardor Backlink Checker a powerful backlink checker with a fantastic simply graphical interface
Try SEOQuake too. I'm not sure if it checks backlinks but it's a free Firefox add-on that's got a lot of cool SEO features. Hope that helps. Have a good day!
Why don't you add your site to google webmaster tool. Its free, can export backlinks to CSV and find maximum backlinks crawled by google bot. But you can get a list of backlinks of the site owned only by you.
There are many tools by which you can find back links but i think backlinkwatch is one of the best software to find back links.