ItsonlikeDonkeyKong:
I wish I could remember the source, but one figure I saw was that between 30,000-40,000 Canadians served in the US Forces in Vietnam. Australian, South Korean, Thai, and New Zealand Army forces also served in Vietnam. Supposedly, there was also a handful (less than 12) Spanish military advisors in Vietnam, working with the US.
There must have been other nations in the Southeast Asian/Pacific Rim region who felt threatened by the spread of communism in their backyard.
I don't know if you're aware of this, but when Suharto was the dictator of Indonesia, he killed every single member of the PKI (Indonesia's own version of the NLF/VietCong), in the country at the time.