I am a US citizen and want to visit Iran. My parents think that I'm being irresponsible; they want to know what happens if I lose my passport. I plan to join a tour group of American citizens (safety in numbers?).
As an American you have to take part in a tour so the hotel normally holds your passport. Your chances of losing your passport in Iran are about the same as losing it anywhere else in the world. Having a photocopy of the data page of your passport along with a copy of your visa is also helpful if it actually is stolen.
But anyhow, if you face any problem in Iran, the US Interests Section in the Swiss Embassy can help you.
Check the cheapest Iran tours.