Why does the core search module not index node titles?
There is a product called Funkywidget


If the title of the node is "Funkywidget" it's searchable by that term. If you want to incorporate search terms that aren't in the node's fields, you should look at more complex search solutions like Apache Solr. 

See here: http://api.drupal.org/api/drupal/modules--node--node.module/function/_node_index_node/6 
The title is added to the search string that's going in the db.

$text = '&lt;h1&gt;' . check_plain($node-&gt;title) . '&lt;/h1&gt;' . $node-&gt;body;