I just had to answer this, especially after viewing other people's responses. A goodly number talked about how they might think there was something to astrology, but they didn't believe in horoscopes.
Now this made me laugh and cry simultaneously, since the horoscope is in fact the prime methodology for preparing an astrological analysis of some sort (personality, present and future trends, horary, and so on - there are many types of analysis that an astrologer can undertake based on a horoscope) and hence is value-neutral, not something one can believe in or not. Whether one can derive insights from a horoscope - the astrological analysis - is another question altogether. But a horoscope is just a method of presenting verifiable facts.
But of course, people have come to believe that the inane and generalised bits of fluff printed in newspapers and the like are "horoscopes," and since they are rarely accurate (although, given the way they are normally developed if the writer of daily newspaper horoscopes really is an astrologer, they will have somewhat more relevance for someoen who was born around sunrise), it is now believed that the horoscope is inaccurate.
So, you may ask, what is a horoscope? Let us examine the word itself. There are twp parts to the word, "horo-" and "-scope."
"-Scope" is a suffix that means viewing or observing. Wikipedia tells us that it "derives from the scientific Latin suffix -scopium, meaning a viewing instrument, which in turn originates from the ancient Greek verb skopein, to examine." This makes sense, we've all heard of telescopes, microscopes, kaleidoscopes, oscilloscopes, stethoscopes, all sorts of scopes. Furthermore, we have likely heard or talked of "scoping" someone or something out. So a horoscope is something that observes or examines, and that may in some sense be thought of as an instrument.
"Horo-" is derived from the Latin "hora," which has the specific meaning of hour, but which can also mean time or season in general. You have horology, the study of timekeeping, and horologe, a (somewhat archaic) word for a clock or timepiece.
So a horoscope can be presumed to be some kind of instrument through which one examines time, or the hour in specific. Once we recall that a horoscope is an astrological instrument, we might make a guess that a horoscope might be a way of examining the planets, sun and moon at a particular time or hour.
Which is exactly what it is. The horoscope is a depiction of where the various planets are in relation to the ecliptic and to the hocal horizon at any given time. If properly calculated and based on accurate measurements, either your own or those published in an ephemeris, there's no belief involved in a horoscope. It just is what it is, a depiction of the planets, the moon and the sun. If I give you a horoscope, and you go to the place it is calculated for, at the time it is calculated for, you will be able to verify (with the aid of telescope) the positions of any planets, the sun, or the moon, that are shown to be above the horizon on the horoscope. To verify the position of anything below the horizon, you will have to be in instantaneous communication with someone exactly opposite you, in terms of longitude and latitude, who is also looking at the sky.
Certainly there is considerable debate as to what the horoscope means. That's the analysis, and some people think it means absolutely nothing, and others think it has anywhere from a limited to an overwhelming meaning. But an astrologer and an astronomer, once they agreed on some technical definitions having to do with terminology for divisions of the ecliptic and the local meridian, would come up with the same diagram.
So do I believe in horoscopes? The question is meaningless.
Do I think that horoscopes can be interpreted using astrological principles to provide useful information about something that may have happened or someone who may have been born at the precise time and place for which a horoscope is calculated? Now that's the question.
I learned to calculate horoscopes and interpret them according to astrological principles at the age of 18, and in fact did this professionally for a good 15 years of my life. While retired from practice, I still do horoscopes and off-the-cuff interpretations for friends. Over 34 years, I've developed my own thoughts on why the interpretation of horoscopes in this fashion has a certain degree of relevance and meaning, and I've refined some of the principles I was taught to fit my personal hypotheses. And after all of that, the answer for me is still yes.