How to minimize a window to the taskbar? (i.e. not iconify)

That icon on the taskbar is the icon of the Application (Handle) rather than that of the MainForm.

Use:

Application.Minimize;

Edit: But out of both your links, I understand you knew that already...duh ;)

This works for the MainForm:

TForm1 = class(TForm)
private
  procedure WMSysCommand(var Msg: TWMSysCommand); message WM_SYSCOMMAND;
protected
  procedure CreateParams(var Params: TCreateParams); override;

...

procedure TForm1.CreateParams(var Params: TCreateParams);
begin
  inherited CreateParams(Params);
  with Params do
  begin
    ExStyle := ExStyle or WS_EX_APPWINDOW;
    WndParent := GetDesktopWindow;
  end;
end;

procedure TForm1.WMSysCommand(var Msg: TWMSysCommand);
begin
  if Msg.CmdType = SC_MINIMIZE then
    ShowWindow(Handle, SW_MINIMIZE)
  else
    inherited;
end;

And to hide Application.Handle from the taskbar (to only have a taskbar icon for the MainForm): set the Visible property of this Form to True and hide the Application in the project file:

Application.Initialize;
Application.CreateForm(TForm1, Form1);
ShowWindow(Application.Handle, SW_HIDE);
Application.Run;

For this form, ShowWindow(Handle, SW_MINIMIZE); shóuld work. It also provides for the default zooming-feature of Windows when minimizing or restoring.

(Tested with D5 & D7 on XP and W7)