You can use jQuery.getJSON and append &output=json to get the data in JSON format.
Then, you can easily parse the returned data as follow:
$.getJSON('http://where.yahooapis.com/v1/countries?appid=w1u_hHfV34HRdninyHHdnigDEeGV9x4PnbnsKOw4&output=json', function (data) {
for(var i in data.places.place){
$('#Country').append('<option value="'+data.places.place[i]['woeid']+'">'+data.places.place[i]['name']+'</option>')
}
});