You are going to have to change somewhere as I don't think there are any non stop flights to Vietnam as yet. Depending on which airline you fly with you will normally have to change at Singapore, Bangkok or Kuala Lumpur.
If you want to do a tour of the country it is probably best to fly into Hanoi, then make your way south, if you are wanting to see just the south, the mekong delta and beaches then fly to Ho Chi Minh (Saigon).
I flew with Lufthansa a couple of years ago and had to change at Frankfurt, then the plane stopped at Bangkok where we all had to get off for about an hour, got back on the same plane and had a short flight to Saigon. It was in all a long cramped flight.
For long distant flights Malaysia Airlines and Thai Airlines have the most
comfortable seats.
I believe that it is sometimes cheaper to book a flight to any of the above major cities with one of the large airlines(mentioned above) then get a cheap flight with a local airline for example, Bangkok Airlines or Silkair. Haven't done that myself but I am sure one of the regular Far East poster's will be able to give you some info.

We flew into Saigon from hong Kong so can't help. However, we flew on to Bangkok with Lufthansa and, as Judith said, most were flying on to Frankfurt. I would not have enjoyed my flight with them- cramped, no seat back tvs. Ok for the hour we had though!

I am looking at Vietnam for summer 2007
Will probably visit Hanoi, Hoi An , Nha Trang then HCMC.
Definately a fast growing tourist destination - kuoni have just launched thier 1st ever dedicated Indochina brohure - some interesting itineraries in there - I quite fancy a DIY holiday though, just a bit worried about just how rainy it will be in summer.

remember you need to send away for a visa giving exact dates of your stay.