A common reference point as to why people believe the advice of psychics and astrologers - not to mention many other nice things said about them - is the "Barnum Effect." Named after P.T. Barnum, the name 'Barnum Effect' comes from the fact that Barnum's circuses were popular due to their having "a little something for everyone." A misquote often attributed to Barnum, "There's a sucker born every minute," is not the source of the name but is arguably relevant.
The Barnum Effect is a product of people's predilection to believe positive statements about themselves, even when there is no particular reason to do so. It is an issue of selectively noticing the things which are preferable while ignoring those things which are not. Studies of how people receive astrological predictions have revealed the influence of the Barnum Effect.
For example, C.R. Snyder and R.J. Shenkel published an article in the March, 1975, issue of Psychology Today about a study of astrology which they performed on college students. Every member in the group of students received the exact same, vaguely worded horoscope about their characters and all the students were very impressed with how accurate it sounded. A few were asked to explain in more detail just why they thought it was accurate - as a result, these students thought it was even more accurate.
At Lawrence University, psychologist Peter Glick along with some of his colleagues performed another study on students there, first dividing them into skeptics and believers. Both groups thought that their horoscopes were very accurate when the information was positive, but only the believers were inclined to accept the validity of the horoscopes when the information was negatively worded. Of course, the horoscopes were not individually prepared as they were told - all of the positive horoscopes were the same and all of the negative ones were the same.
Finally, an interesting study was performed in 1955 by N.D. Sunberg when he had 44 students take the Minnesota Multiphasic Personality Inventory (MMPI), a standardized test used by psychologists to evaluate a person's personality. Two experienced psychologists interpreted the results and wrote personality sketches - what the students received, however, was the real sketch and a fake one. When asked to pick the more accurate and more correct sketch, 26 of the 44 students picked the fake one.
Thus, more than half (59%) actually found a fake sketch more accurate than a real one, showing that even when people are convinced that a "reading" of them is accurate, this is absolutely no indication that it is, indeed, an accurate evaluation of them. This is commonly known as the fallacy of "personal validation" - an individual cannot be relied upon to personally validate such estimations of their fortune or character.
The truth seems clear: whatever our backgrounds and however rationally we may tend to act in the normal course of our lives, we like to hear nice things said about us. We like to feel connected to people around us and to the universe at large. Astrology offers us just such feelings, and the experience of getting a personal astrological reading can, for many people, impact how they feel.
This is not a sign of stupidity. Quite the contrary, the ability of a person to find coherency and meaning in a variety of disparate and often contradictory statements can be seen as a sign of real creativity and a very active mind. It requires good pattern-matching and problem-solving skills to develop a reasonable reading from what they are normally given, so long as the initial assumption is granted that the reading should be expected to provide valid information in the first place.
These are the same skills we use in order to derive meaning and understanding in our daily lives. Our methods work in our daily lives because we assume, correctly, that there is something meaningful and coherent out there to understand. It is when we make the same assumption incorrectly and in the wrong context that our skills and methods lead us astray.
It is not really surprising, then, that so many continue to believe in astrology, psychics and mediums, year after year, despite the ample scientific evidence against them and general lack of scientific evidence to support them. Perhaps a more interesting question might be: why don't some people believe such things? What causes some people to be skeptical more consistently than others, even when being credulous feels good?