I have traveled enough to know that checking visa and immunization requirements is the first thing you should do before traveling.
Now I just arrived in Vietnam yesterday. I was convinced I can just get my Visa on Arrival like in Indonesia. This was reconfirmed by nobody raising any issues when checking in or boarding. Alas for Vietnam you will need a letter of approval that is issued by many agencies for a minimal cost.
What is visa on arrival?
This is an alternative way to get your visa for Vietnam. You just need to fill in our "Online Application Form", pay the service fee, get your "Visa approval letter" within 2 working days and pick up your visa at your destination airport (Hanoi airport, Ho Chi Minh city airport) –
After we obtain the approval letter for you, we will forward you a copy by email. Copies of the same document will be forwarded on your behalf to Vietnam Immigration checkpoints at International Airports only. When you arrive in Viet Nam, the Immigration officers will have those documents ready and will be able to issue your entry visa quickly. (See our guide to visa procedure at Vietnam airports)
So what happens if you show up without the approval letter at the airport?
Initially I was offered a ride back with the same airplane I just arrived but I'd have the same issue since the usual approval process takes 2 days. However there is a shortcut in Ho Chi Minh airport at least. They have a travel agency that is able to provide the paperwork and approval letter on the spot. The pleasure of the service will cost you $115 + regular visa fee. It's still reasonable considering normal visa fees for China or India but steep considering South East Asia's easy visa policies.
The whole process took a long time since it wasn't clear initially that this would be a way to go and the officer only reluctantly agreed to that. Plus there were a number of flights landing at the same time with 200+ people waiting for the visa stamp in there passports.
After a couple of hours I was able to enter Vietnam finally.
So the good news is that you can enter Vietnam without the approval letter and any preparation with a US passport. The bad news is that it will set you back $115 + the visa fee.