JQuery$.ajaxは、ネイティブ メソッドを介してキャンセルできる xmlHttpRequest オブジェクトを返します。.abort()
$("#search").autocomplete({
    minLength: 3,
    delay: 300, // this is in milliseconds
    json: true,
    source: function(request, response){
        // New request 300ms after key stroke
        var $this = $(this);
        var $element = $(this.element);
        var previous_request = $element.data( "jqXHR" );
        if( previous_request ) {
            // a previous request has been made.
            // though we don't know if it's concluded
            // we can try and kill it in case it hasn't
            previous_request.abort();
        }
        // Store new AJAX request
        $element.data( "jqXHR", $.ajax( {
            type: "POST",
            url: "foo.php",
            dataType: "json",
            success: function( data ){
                response( data );
            }
        }));
    }
});