I'll be in Saigon the middle of June for about a week, and will travel form there to Bangkok. What travel agencies or airlines could you advise using? What are airfares running 1 way? Many thanks!

Check AirAsia. They were suppose to start service between SGN and BKK in November06. Very cheap and realiable service. I know they fly out of Hanoi. Easy to book on line. One way fares for under $100USD
Thai airlines usually for $170-$250USD RT
Viet Nam airlines
Lufthansa has flights that stop there on the way west. Sometimes offering pretty cheap one way flights
Most any agency on De Tham street/Pham Ngu Lao area can help you out. Shop around.
good luck
Both Thai and Vietnam airlines fly that route. Try booking your flight with Vietnam Airlines directly to avoid the additional 3-4% booking fee most agents charge.

I wasn't aware of the AirAsia service between SGN and BKK. Great advice, thanks to you both.

I was in March in Saigon and I took a flight to BKK with Vietnam Airlines. It cost around 200USD. Airasia didn't fly at that time to BKK..
Lena
You weren't aware of the Air Asia service because it doesn't exist. They still are only flying to Hanoi. You should also check Bangkok Airways. They fly 3 times/week to between BKK-SGN.

Pacific Airlines, a Vietnamese carrier that recently morphed into a budget airline flies from SGN to BKK. AirFrance has some special low fares on this route as well.