"Questions that may already have your answer" Stackexhange Module For Drupal
If a 'Question' is a node, you could use the Similar Entries module as a starting point:


  Similar Entries provides lists of links to site content related to the current node being viewed. Links can be displayed in standard blocks or as part of custom views. Similar content is located and rated using MySQL's FULLTEXT indexing for MyISAM tables. FULLTEXT is a special query that helps find relevant content in other nodes using a natural language search that interprets the search string as a phrase in natural human language.


It will require some customisation to get a similar workflow to the one Stack Exchange uses (you'll need to make the blocks appear on the node add/edit pages somehow, and implement an AJAX solution for suggestions while writing the title).

I'd be surprised if there's a module which replicates the functionality here straight out of the box.