Have you tried backlinkwatch.com? It works pretty good, it's free and it shows anchor text (if any) and which links are nofollow.
Your best bet is probably the Google Webmaster tools. It's fairly reliable and will show you which links that Google considers as pointing to your website.
you can this site for checking your backlinks: - http://ahrefs.com - http://majesticseo.com - http://opensiteexplorer.org
Search engines provide many backlink checker tools.When we submitt our website url in this tool.This automatically check backlinks..
I use the website backlinkanalyze.com but you can only scan once a week unless you buy premium. I find it has the same accuracy as open site explorer, but a lot cheapper!
If I were you use the Google webmaster tools, I have used huge numbers of backlink checking website but all seem to come back with varying results which is very confusing!
SEO Pro’s Link Checker This is a very fantastic backlink checking service. Although it takes a little while (not too long) to populate the list of URL’s, this is one of the few tools in this whole list that actually shows the true pagerank of the pages your URL is on.
Backlinkwatch and Webmaster are both pretty good. The thing is you'll find varying links found from various services. It serves to give you a good overall idea but you can't take it as the absolute number. In fact, I've seen sites jump in rank during a link building campaign before they've actually been counted "publicly" through any aggregator or service.