Watching a report on Jim Webb, and it occurred to me that Vietnam is the only major war which we have not had a president who served in it. I don't think Webb has a major chance in 2016.
PS. I'm not really counting Bush 43. I don't think he was ever in Vietnam.
The Korean War isn't major enough for you?
Carter served on a submarine in the Pacific during the Korean War. It depends how closely you want the service to be related to the theatre of war.
Carter never seen combat (after WWII, hardly any submariner did) and AFAIK he wasn't close enough to Korea to be regarded as participant of the conflict.
If we use this definition, any soldier/sailor/airman/marine serving in the Pacific would count as Korea and Vietnam vet, even if they served miles away and had no connection.