Untitled

document.write(fbResults.cats[0].title);

<!DOCTYPE HTML>
<html>
<head>
<title></title>
<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.7.2/jquery.min.js"></script>

<script>

    $(document).ready(function() {
        $.getJSON('http://mydomain.com/api/get_cats', function(fbResults) {
            document.write(fbResults.cats[0].title);
        });
    });
</script>

</head>
<body>

</body>
</html>

{"cats":[

{"id":"1","title":"mytitle1","colour":"#EE297C"},
{"id":"2","title":"mytitle2","colour":"#EE412F"},
{"id":"3","title":"mytitle3","colour":"#F5821F"},
{"id":"4","title":"mytitle4","colour":"#00AEEF"},
{"id":"5","title":"mytitle5","colour":"#00B495"},
{"id":"6","title":"mytitle6","colour":"#006476"}

]}

$('body').append('<p>'+fbResults.cats[0].title+'</p>');

$.each(fbResults.cats,function(index,item){
    document.write(item.title);
  });

<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />