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

 {With FindWindow, GetWindowRect }

 type
   TTaskBarPos = (_TOP, _BOTTOM, _LEFT, _RIGHT, _NONE);

 function GetTaskBarPos: TTaskBarPos;
 var
   hTaskbar: HWND;
   T: TRect;
   scrW, scrH: integer;
 begin
   hTaskBar := FindWindow('Shell_TrayWnd', nil);
   if hTaskbar <> 0 then
   begin
     GetWindowRect(hTaskBar, T);
     ScrW := Screen.Width;
     ScrH := Screen.Height;
     if (T.Top > scrH div 2) and (T.Right >= scrW) then
       Result := _BOTTOM
     else if (T.Top < scrH div 2) and (T.Bottom <= scrW div 2) then
       Result := _TOP
     else if (T.Left < scrW div 2) and (T.Top <= 0) then
       Result := _LEFT
     else // the last "if" is not really needed 
    if T.Left >= ScrW div 2 then
       Result := _RIGHT;
   end;
 end;

 procedure TForm1.Button5Click(Sender: TObject);
 var
   TaskBarPos: TTaskBarPos;
 begin
   TaskBarPos := GetTaskBarPos;
   case TaskBarPos of
     _LEFT: ShowMessage('Left Position');
     _TOP: ShowMessage('Top Position');
     _RIGHT: ShowMessage('Right Position');
     _BOTTOM: ShowMessage('Bottom Position');
   end;
 end;