Ben Bova has written an impassioned editorial praising the story , while PZ Myers at Pharyngula writes an equally impassioned criticism.
It was a very popular story, but the reason isn't complimentary: it fed into a strain of self-serving smugness in science-fiction fandom, the idea that people who read SF are special and brilliant and superior, we are the technological geniuses and far-seeing futurists, while the mundanes leech off our vision. The eugenics movement built on the same us-vs.-them mentality, that there are superiors and inferiors, and the inferiors breed like cockroaches. The most troubling part of it all is the attempt to root the distinction in biology—it's intrinsic.
My feeling is that the story is fundamentally wrong about the nature of intelligence. People frame the issue as if intelligence were either genetically determined, or the result of environmental factors such as education. In both cases the individual is passive. In my opinion intelligence is much more a matter of will, or to put it another way, responsiveness to social pressure. To be intelligent is to apply your energy and attention to problem solving, within a given context. Almost any individual can decide to be 'intelligent' (usually in a particular field) at a cost of some stress and frustration, and sometimes social isolation. These individuals then feel a certain amount of self-congratulation at being 'smarter' than other people; they might even believe they are genetically distinct from the rest of the population.
Anyway, leaving my theories of intelligence to one side, I think 'The Marching Morons' is an example of an important but not very pleasant SF story, which still evokes passionate controversy fifty five years after it was published. It is possible the author wrote it with this satirical intention.