Vietnam is a relatively safe country to visit. That said, there are increasing instances of theft, especially in HCMC where pickpockets and snatch thieves on motorbikes are the worst menace. The best tip is to be vigilant at all times. Often cute kids or old grannies have deft fingers. Leave all valuables (expensive watches, jewellery, glasses, etc.) at home, and don’t even wear flash costume jewellery. Make sure you have a firm grip on cameras and shoulder bags at all times and never leave anything you value lying around unattended. I would also not advise taking cyclos late at night, especially in HCMC.
The other problem area is on the trains, especially the night trains from Hanoi to Lao Cai. Again, make sure all your luggage is safely locked, preferably stowed out of sight or attached to an immovable object, and don’t leave things near open windows. It’s also wise not to accept food or drink from people you don’t know (there are reports of one or two people being drugged and robbed this way).
You might also have read warnings about unexploded shells, mines and other ordnance lying around. This is still the case in the DMZ, around My Son and certain border areas, particularly along the Chinese border. It is advisable to visit such areas only with an experienced local guide and never stray off well-trodden footpaths anywhere in Vietnam.
Finally, there’s the traffic. Trying to cross the street in Hanoi or HCMC is an adventure in itself! You’ll be faced with a tightly-packed stream of scooters, bikes and cyclos which looks completely chaotic at first. But don’t give up! Either walk till you find some traffic lights or just go for it. The key is to walk slowly and steadily out into the traffic. As long as you keep a steady pace and make your movements clear, the traffic will flow round you. Problems arise if you stop or move too quickly and the drivers/riders can’t anticipate your progress.
But don’t get paranoid! Thousands of people visit Vietnam each year without experiencing any problems whatsoever. It’s also worth bearing in mind that the situation in Vietnam is certainly no worse than many big European and American cities. Just take the same precautions you would in any unfamiliar place, and you should be fine.