Does Google, Bing, or any of the other major search engines make a list or index of related search terms available?
There is the Google Adwords Keyword Tool
Yahoo Boss has an API that provides related search terms. Check out the API Response Fields: http://developer.yahoo.com/search/boss/boss_guide/ch02s02.html
Google's Custom Search API has related search terms in their Refinement Labels: code.google.com/apis/customsearch/docs/refinements.html
Granted these aren't exactly the same related search terms that you'll find on Yahoo.com and Google.com, but they're pretty close and of course the same engineering teams worked on the algorithms being used.