Karbala and Najaf: as you might imagine, visiting these Shia shrine cities is a bit of serious business. There is major pilgrim traffic in both, and a completely different atmosphere to Baghdad or Mosul. Both draw millions of visitors every year from all over the Muslim world, to pay their respects at the tombs of Ali, Hussain, and Abbas. Religious pilgrim or not, if you're traveling in Iraq you will want to go to them both, too.