As expected Yahoo will be closing down Yahoo Site Explorer this year. Yahoo has just announced the date for the closure. This coming Monday, November 21, 2011, Site Explorer will cease to exist.
The short Yahoo blog post reads:
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!. Site Explorer services will not be available from November 21, 2011.
Bing Webmaster Tools has much of this information, with the big exception of competitive linkage data, which is a huge exception.
There are third party tools including Majestic SEO and SEOmoz but with the loss of Site Explorer, there will likely be no search engine-provided look at your back links.