$("#cboPais").change(function () {

    var params = new Object();
    params.pais = $("#cboPais").val();
    params = JSON.stringify(params);

    $.ajax({
        type: "POST",
        url: "SociosRed.aspx/GetDepartamentosByPais",
        data: params,
        contentType: "application/json; charset=utf-8",
        dataType: "json",
        async: false,
        success: function(LoadDepartamento){
            console.log(LoadDepartamento);},
        error: function (XMLHttpRequest, textStatus, errorThrown) {
            alert(textStatus + ": " + XMLHttpRequest.responseText);
        }
    });

});

function LoadDepartamento(result) {

$("#cboDepartamento").html("");


$.each(result.d, function () {
    $("#cboDepartamento").append($("<option></option>").attr("value", this.Codigo).text(this.Nombre))

});}

<asp:DropDownList ID="ddlContinents" runat="server" AppendDataBoundItems="true"
         onchange = "PopulateContinents();">
    <asp:ListItem Text = "Please select" Value = "0"></asp:ListItem>
</asp:DropDownList>

[System.Web.Services.WebMethod]
public static ArrayList PopulateCountries(int continentId)
{
    //codigo
}

$.ajax({
        type: "POST",
        url: pageUrl + '/PopulateCountries',
        data: '{continentId: ' + $('#<%=ddlContinents.ClientID%>').val() + '}',
        contentType: "application/json; charset=utf-8",
        dataType: "json",
        success: OnCountriesPopulated,
        failure: function(response) {
            alert(response.d);
        }
    });