People fear communism because many of the countries that have had it have been totalitarianism regimes. People associate communism with China and Russia often, and they were the enemies of freedom. Therefore, communism got modified and adapted a lot.
People generally feared the lack of freedom to live their lives they way they wanted to. This included the freedom to assemble and protest, the freedom to work where they wanted to, and to have the ability to grow their wages. It also involved the freedom to travel, and the freedom to worship (if they were of a faith) where they wanted to, when they wanted to, and how they wanted to.
Communism limited private ownership, which meant many people were not motivated to expend time and energy and resources to serve only the authoritarian government over them. This contributed to a lack of innovation and less efficiency among the working class. As stated in Post #2, people did abhor the lack of political freedom, and the curbs (censorship) concerning freedom of expression, whether by word, by art, in print or by any other means.
Part of the communist purpose was to encourage and enable the working class, the proletariat, to rise up against the state and take over the means of production. In a capitalist society like ours, this would amount to a full-scale revolution. As countries like Russia, China, Vietnam, and Korea became communist, it must have looked to the United States like we were holding back a surging movement intent on destroying our way of life (this was known as the domino theory).
People feared communism because they did not want to lose their rights. Communist governments typically deny people the right to freedom of speech and to political participation. They also deny people the right to do what they want with their own property. Most Americans would not like to live in a society that denied such rights.