Having been organising tours to Iran since the 1990's we have often been asked the above question. From the experience we have had it is a very safe destination. The people are very hospitable and actually like to meet and talk to foreigners especially North Americans. We have regular tours to Iran and we cover all the major sites that are of importance and have never encountered a situation that could have made us think otherwise.
Will be interested to hear from anybody who has other or similar experiences.