Ask 100 soldiers, get 50 different opinions. This war lasted for nine years, and had both volunteers and draftees, involved all branches of the military, and nearly 8 million Americans who served during that time, so I don't think you can generalize any one feeling among soldiers about the war.
I think you can say there were more soldiers who favored the war in the early years than they did after 1970. I think you can say that, among draftees, most just wanted to serve their time, do their best and come home, whereas you often find that with volunteers, they served more than one tour (especially true among helicopter pilots, see Robert Mason's Chickenhawk).
My feelings about the war remained fairly positive and I served 1969 through 1970. My opinion was that the Vietnamese tolerated us. I worked with Ruff-Puffs for most of my time. I had one ARVN Marine tell me at Freedom Hill "it's hard to hate a person who gives you money if they think they screwed somebody over".
It was clear to us that U.S. was washing its hands of the war. No one wanted to be the last man to die in a war that politicians, brass, and people wanted out of.
When the NVA overran the South, I got extremely drunk, "For What"? I lost friends over there, and they died for nothing?
I would agree with the last post in that it depended on when they served. Early in the War it was accepted opinion that we were there to help oppressed people against an aggressor. As the war drug on the feelings definitely changed. I think that a lot of it was influenced by the media and their coverage of the war.
The first two answers are not completely incorrect, but they do not pay enough attention at all to the variation in attitudes among American soldiers, especially across time.
Most importantly, we must note that unhappiness among the soldiers was a phenomenon that was seen late in the war. I would say, generally speaking, that it was confined to at least the time after 1969. This is partly due to the fact that the war was not clearly going badly until after the Tet Offensive of 1968.
Up until that time, there was a great deal more support for the war, both in the United States and among its soldiers. The picture of the drugged-up draftee trying to kill his officers in battle is seen as typical, but it is really more of a thing from the end of the war. Let me close with a quote from eNotes' discussion of the attitudes of American soldiers:
During the early years of the war, many American servicemen supported the U.S. government's decision to become involved in Vietnam. They believed it was important to stop the spread of communism in Southeast Asia. As a result, the morale of American troops was fairly high—at first. By the late 1960s and early 1970s, however, both the morale and performance of the U.S. forces declined rapidly.
The Vietnam War was one where young men from USA were forcibly deployed in the army. This was a starting point for the anger that was to build up in them.
In Vietnam, the soldiers did not feel the work they were doing there in saving the Vietnamese was being acknowledged by the people they were doing it for. That was another reason for the rage that built up within a majority of the soldiers. They saw the Vietnamese as people who were colluding with the Viet Cong and trying to harm the soldiers. This feeling led to all the atrocities that American soldiers committed against the Vietnamese.
Soldiers also had to face a very harsh weather, totally unlike what it is in the US. Their life was divided into long intervals of having to do nothing but fend against the weather and the rough environment and short unpredictable intervals of actual battle with the enemy.
The tough life that soldiers had and the lack of acknowledgement of their hardships both by those they were protecting as well as by people in the America, who thought of the soldiers as drug addicts and losers created a deep sense of frustration among almost all the soldiers who were posted in Vietnam.
Certainly, as with any war, one will find divergent examples of soldiers' impressions of it. Yet, I think that the Vietnam War featured a high number of soldiers experiencing resentment at their time of service and disappointment as to why they were asked to fight. The establishment of the organization of Vietnam Veterans Against the War might speak to this. One does not see similar organizations dedicated to the fight in World War II. This particular organization captures a sentiment that the war was improperly commissioned and soldiers were sent in harm's way for little reason. The organization serving as a bastion for soldiers' resentment and anger towards the war is very notable. It helps to bring out how many soldiers felt about the policies that started the war and the practices that put soldiers in difficult conditions. I think that much of for what the organization stands helps to bring out a contingent of soldier feelings towards the war.