Anonymous delegates make the code much more readable in some case (you don't have to go to another method to see code that belongs to your method:
Winforms example
class MyForm:Form{
//...
protected override void OnLoad(EventArg e){
this.Cursor=Cursors.Wait();
this.Enabled=false;
// do a long running DB operation without blocking the UI Thread
ThreadPool.QueueUserWorkItem(state=>{
DoLongDBOperation();
// re enable the form
BeginInvoke(new Action(()=>{ this.Cursor=Cursors.Default;this.Enabled=true;}));
});
}