In reply to blotterhound2:
Neither in their entirety. My wife wrote the Cicerone guide and describes it anti-clockwise. She's walked it in both directions numerous times but has a slight preference for clockwise. You have to think about which sections you'd prefer to walk downhill or uphill, which sections it might be better to miss out (! - think ski installations, pistes etc) by taking a lift. Whether you want to leave the highest pass till last or do it first and risk feeling bad with the altitude. Where you want to start/finish - Zermatt is expensive and crowded - Grächen, Saas Grund or Randa, for instance, are quieter and a little cheaper (though this is Switzerland of course...) or start/finish in Italy - Gressoney, for instance, easily accessed from Turin or Milan.