What happened to yahoo site explorer? Is there another program I can use to check my website's or other website's backlinks?
It's gone and now Yahoo! uses Bing as it's source for search results. So, just sign up with Bing's Webmaster Toolbox for something similar (to check your own and of course Google's Webmaster Tools allows you to check your own, too). Otherwise, you can use OpenSiteExplorer.org (you can do several queries for free each day, I believe), majesticseo.com and ahrefs.com (among others).
I use backlinkwatch.com for checking backlinks of my sites now, it provides accurate information... and it is popular too.
Yahoo! Site Explorer was a Yahoo! service which allowed viewing of information on websites in Yahoo!'s search index. In particular, it was useful for finding information on backlinks leading to a given website or domain. The service was closed on November 21, 2011 and merged with Bing Webmaster Tools, a tool similar to Google Webmaster Tools.
Use ahrefs.com tools. I'm using it after Yahoo! Site explorer shut down. You can also use OpenSiteExplorer.org