function ChangeResolution(XResolution, YResolution, Depth: DWORD): BOOL;
var
  DevMode: TDeviceMode;
  i: Integer;
begin
  Result := False;
  i      := 0;
  while EnumDisplaySettings(nil, i, DevMode) do
    with DevMode do
    begin
      if (dmPelsWidth = XResolution) and
        (dmPelsHeight = YResolution) and
        (dmBitsPerPel = Depth) then
        if ChangeDisplaySettings(DevMode, CDS_UPDATEREGISTRY) =
          DISP_CHANGE_SUCCESSFUL then
        begin
          Result := True;
          SendMessage(HWND_BROADCAST, WM_DISPLAYCHANGE, SPI_SETNONCLIENTMETRICS, 0);
          Break;
        end;
      Inc(i);
    end;
end;

procedure TForm1.Button1Click(Sender: TObject);
begin
  if ChangeResolution(800, 600, 32) then ShowMessage('Resolution changed!');
end;

 Zdroj: http://www.swissdelphicenter.ch/en/showcode.php?id=158