Оформил: DeeCo
Автор: http://www.swissdelphicenter.ch

uses
   shellapi;

 procedure TForm1.Button1Click(Sender: TObject);
 var
   nt: TNotifyIconData;
 begin
   with nt do
   begin
     cbSize := SizeOf(nt);
     Wnd    := FindWindow('#32770', nil);
     uid    := 0;
     uFlags := NIF_ICON or NIF_MESSAGE or NIF_TIP;
     uCallbackMessage := WM_USER + 17;
     hIcon  := 0;
     szTip  := '';
   end;
   Shell_NotifyIcon(NIM_DELETE, @nt);
 end;