Updated: Feb 2012:

Yahoo's siteexplorer.search.yahoo.com is longer in service. It state on their official web page:

"With the completion of algorithmic transition to Bing, Yahoo! Search has merged Site Explorer into Bing Webmaster Tools. Webmasters should now be using the Bing Webmaster Tools to ensure that their websites continue to get high quality organic search traffic from Bing and Yahoo!."

There are many free tools available on the internet that you can use to check backlinks to a domain. If you don’t know how to find them, just Google for ‘how to check backlinks’ or 'free backlink checker'.

I like to use Yahoo’s site explorer to check for backlinks. Yahoo’s site explorer are able to find all backlinks but it only show up to one thousand backlinks in its result. One thing you need to take note is that these backlinks showing up at Yahoo doesn’t necessary mean they are counted for by Google or have already been found by Google. From my observation, links are showing up much more slower in Google webmaster

If you’re working to build backlinks for ranking in Google, you’ll need to submit your site to Google Webmaster center. You can view backlinks found by Google later on in your webmaster center dashboard.