I'm far from an expert but in the preface to "The Communistic Societies of the United States" by Charles Nordhoff, Franklin Littell gives a list of historical factors that helped give rise to this phenomenon.
There was a fever of social optimism and experimentation. People were wondering what America could become and felt that developing models of social interaction was a way of answering that question. As well many utopian groups were also european groups who had begun social experimentation in their native countries and faced persecution for it. America was so vast and unregulated that they could continue those experiments with much more freedom.
Survival at the frontier was difficult and groups of strong cooperators did better than individualists. Without much access to law or institutions groups had to design strong sets of social norms in order to maintain cooperation and prevent defection.
Utopian communities were attractive to young women. Shaker and Mormon communities often had many times more female than male converts. Frontier life could be brutally hard and isolating while a common observation made by Charles Nordhoff in the text of the book was that "the members do not work hard...I have found it generally true that the members of communistic society take life very easy". The community structure and many hands make light work communitarianism of utopian communities may have been more attractive than constant drudgery and pregnancy (many utopian communities were celebate in that period).
Communities in that period were largely oasises. Distances between settlements were often so vast that communities did not find it any "difficulty in finding space to settle in or in enforcing their own peculiar disciplines upon members".
Hope that helps and I'm looking forward to others chiming in on this question.
If I could tag along; which experiment do you (as a historian) find the most interesting?
America was seen as a potential Utopia since at least the time of Francis Bacon's "The New Atlantis" in 1627. Some of the early English Colonies, especially the New England Colonies, were specifically established to be modeled on what can be described as Utopian ideals.
The early 1800's of course were a couple of Centuries later; however the vast continent had not yet been settled (by people of European descent) and there still was room enough for people to project their own idealistic visions upon what was perceived to be a wide open landscape, far from the interference of external authorities. And in doing so, they were continuing what the Pilgrims and others had started long before.