Every country in the world has its share of potential dangers, but security in Hoi An is generally at an adequate level. While petty theft in public places is not uncommon, you can easily avoid it by following some basic safety precautions.
When going on a tour, it's advisable not to bring jewelry or valuable items with you. Instead, leave them in the hotel safe. It's also a good idea to have a copy of your passport and try not to draw unnecessary attention to yourself.