HCMC is considered as a high class city in Vietnam. In fact, this is the most modern and livable places in the country and is definitely a safe place to reside. Violent crimes perpetrated against expats or foreigners is virtually unheard of as it is next to impossible to acquire a firearm. Petty scams, theft, and pick pocketing or bag snatching are the most commonly reported crimes so just like when you're travelling anywhere around the world, one of the best tips for foreigners is always to use your common sense. Be aware of your surroundings and mind your belongings when in crowded public areas to avoid these crimes.
Vietnamese neighbours loath criminal behaviour and have a habit of taking care of each other. Most often, they end up chasing down fleeing suspects and dispensing vigilante justice as they see fit. Having said that, many homes in the city are fortified against break-ins and protected by high walls, lockable door gates and window bars.
For information on living in Saigon go to Saigon: Not Yet a Tourism Hub