XElement x = XElement.Load("contactlist.xml");
var ken = x.Elements("contact").Where(n => n.Element("name").Value == "Ken");
ken.Remove();
x.Save("contactlist.xml");
In VB.NET:
Dim x As XElement = XElement.Load("contactlist.xml")
Dim ken = x.Elements("contact").Where(Function(n) n.Element("name").Value = "Ken")
ken.Remove()
x.Save("contactlist.xml")