According to Islam it's wrong to believe in horoscopes, divination, or any superstitious bullcrap (including "rub this for luck" attitudes etc.). Islam encourages the study of Astrology as a science not as a divination support argument. Technically, Islam encourages the pursuit of knowledge in general.
While Astronomy is the study of cosmic events (an actual science), Astrology is often treated as a pseudoscience for divination; the reality of the study is philosophical and psychological rather than the superstitious "mumbo jumbo" it's commonly portrayed as. Dismissing Astrology would be like dismissing Mythology as a legitimate field of study. However I do agree with Cobra that people who claim to believe in astrology are mesmerized by the mysticism rather than any argument of common sense or scientific reasoning that could explain the similarities between people.
I've come a cross more than my share of superstitious nut-jobs who would actually pay to see "psychics," "mystics," and "mediums" (would the plural of Medium be Media?). I've had a fair share of arguments with some so-called "psychics." They seem to be people who get off to the smell of their own farts. I've had someone try to convince me that we were "kindred spirits in a past life" to which I smiled and said "perhaps, but in this life I subscribe to common sense and my trusty instincts."
While I generally choose to be open-minded and receptive to the possibility of the seemingly impossible I firmly believe that no one can foretell the future; at least not beyond common-sense and logical deductions like "keep acting like a jackass and someone's bound to smack some sense into you."
EDIT:
Fun fact: While perusing the WWW I discovered that the archaic term "starcraft" actually means "astrology."
