I’ve never been a big fan of the search auto complete because it usually produces inaccurate results and sometimes leads the user to click on a suggested term that may not be exactly what they were looking for.
Commenting out one single line in your template is all that’s needed to remove the functionality.
Near the bottom – comment out as follows:
var searchForm = new Varien.searchForm('search_mini_form', 'search', '<?php echo $this->__('Enter Keyword(s) to Search ..') ?>');
//searchForm.initAutocomplete('<?php echo $catalogSearchHelper->getSuggestUrl() ?>', 'search_autocomplete');
While your in this code, it’s also an opportunity to change the wording of what appears in the box of a blank form (ie ‘search entire store’ to ‘enter keyword(s) to search’