Edit in JSFiddle

$(function() {
    $('#suggestText').change()
});
$('#suggestText').change(function() {
    $.getJSON('http://suggestqueries.google.com/complete/search?q={0}&callback=?'
              .replace('{0}', $(this).val()), function(data) {
        $('#suggestions li').remove();
        $.each(data[1], function(key, val) {
            $('#suggestions').append('<li><a target="_blank" href="http://google.com/search?q=' + val[0].replace(/ /g, '+') + '">' + val[0] + '</li>');
        });
    });
});

<input type="text" id="suggestText" value="why does my" /> 
<ul id="suggestions"></ul>