Some Alternative Link Checkers
Currently the best alternative, MajesticSEO is a paid link checking alternative that uses their own servers to crawl and index the web. As of now there are several paid options. MajesticSEO is commonly referred to as the best paid link checker.
This is SEOMoz's backlink checker. While it's well designed and user friendly, unlike MajesticSEO, it simply doesn't have the link history or freshness that Yahoo Site Explorer and/or MajesticSEO provides. It's also a paid alternative.
Blekko - Free alternative
Blekko is a boostrapped search engine startup that prides itself on transparency of data and information, including SEO variables.
Head over to Blekko.com, and search for the following as a test. http://www.warriorforum.com /seo
This will show you the SEO information for WarriorForum, you can also dive deeper and look at links by searching
This will give you an idea of where links are coming from, crawl date, IP address of links and other information like NameServer info of incoming links. A valuable tool BUT limited in backlink information.
Did I miss some? Help me fill out the best backlink alternatives by providing who YOU use now that Yahoo Site Explorer has been shut down.