Keep in mind:

It's in your best interests not to drink the tap water, especially after flooding!

Avoid cyclo ride after dark.

Dress modestly and appropriately when visiting local dwellings and religious sites, etc.

Leave your valuables behind before a night out on the town, or going to the beach.

When crossing the road, especially in Ho Chi Minh city, always keep looking to the left and right and walk slowly!

Do not offer money directly to minority people - instead donate to a local charity or offer a small gift, such as pens.

Try at least once the delicious, local street food.

Always ask permission first before taking photographs, especially in minority areas. 

Do not miss:

Sleeping out on deck on a boat in Halong Bay

Ordering custom-made clothes from the local tailor shop

Taking a slow cyclo ride through the French Quarter of old Saigon and Old Street Quarter in Hanoi.

Eating pho ga (chicken noodle soup) at a street side noodle stalls.

Watching the traditional water - puppet performance in Hanoi.

Experience the full moon festivities in the ancient town of Hoi An.

Drinking rice-wine in the minority villages of the north

Taking a boat along Hue's Huong (Perfume) River, visiting the Royal Mausoleums.

Overnight in a home stay in the Mekong Delta's riverside orchards.

Bartering for a bargain at Saigon's largest market, Ben Thanh Market

Taking a stroll through Hanoi's Old Quarters.

Source: Vietnam Administration of Tourism