It is actually quite amazing how many astrologers were skeptics before they became astrologers. I, myself, am the child of a scientist and a mathematician, raised around the chemistry lab. For a long time I thought that astrology was hogwash, because, from a scientific perspective, there is no cause and effect. Stars can't and planets can't possibly cause people to have certain personality traits, I thought, and predicting the future is impossible. But, as a scientist, I also understand the value of empiricism, and I have witnessed far too many astrologers say things that are far too accurate that they couldn't possibly know about clients they have only just met. I don't know why it works, and I don't believe that it should work, but for some reason, I have witnessed it succeed far more often than it fails (indeed, I have never seen it fail, when done correctly).
I myself, while I was still a skeptic, read a few charts, just to see how it would go. Using only the text-book astrology rules, I described my brother's girlfriend (who I had not yet met), and he said my description was perfect. I described my own girlfriend's best friend before I met him, shockingly well. I could go on, but, of course, because that's just my experience, and it's hardly convincing. My point is, though, that my own efforts to determine the validity of astrology surprised me: I convinced myself it works despite an intense bias against it.
It is easy, in this scientific age, to assume that the universe is comprehensible. But the universe, in actuality, is a complicated, convoluted place, and cause and effect is not nearly so well understood as we like to think (the famous empirical philosopher David Hume said as much in his "Treatise on Human Nature," way back in the 18th century, at the height of the Scientific Revolution). I can't think of a rational explanation for astrology, but reason can be overrated.
I would like to say, though, that astrology is driven by mythos more than by astronomy. As many skeptics are quick to point out, the zodiac no longer corresponds to the positions of their original constellations (thanks to the precession of the equinoxes, a phenomenon early astrologers were aware of). But the various signs - though they originally derived their names from constellations - are based more upon time of year than upon any kind of stellar phenomenon. After all, not all of the constellations are the same size to begin with. From the onset, astrologers understood that astrology was terrestrial, as much as celestial.
The mythos surrounding Aries comes from the beginning of spring, while Scorpio is tied to the middle of the fall, and so on. Perhaps mythology does not give a good cause or effect, scientific answer to why astrology works, but it certainly has more to do with its essence than the stars do. Indeed, even the planets are mythical archetypes in astrology, as much as they are literal heavenly bodies. The power of myth, it seems to me, is far less questionable than the power of astrology. Myth rules in religion and literature, and we often value a good story as much as a good meal. Should it be surprising that the stories astrology tells are relevant?
Astrology is a 2,000 year old art (indeed, more than that in some Eastern cultures), and was developed independently by a variety of civilizations, with a high degree of compatibility from one system to another. Astrology is responsible for concepts like "weeks" and "months," and gave us the names of most of the days (Monday and Sunday being the most obvious). Above all, though, astrology has been adaptable and responsive to scientific discovery (whether that meant introducing new planets as they were discovered, and accounting for significant asteroids and other phenomena near or on the ecliptic, or developing new mathematical and emperical systems for casting charts), and despite the hostility directed at it for centuries, it has maintained a steady following. Perhaps it is not all true, and perhaps it does not work for everyone - that I cannot know - but enough people find solace in astrology, or find personal insight, or, at the least, find entertainment, to sustain the study. I think that speaks to accuracy of astrology: why else would so many people continue to visit astrologers, time and time again?
I assure you, at the very least, that there are many well-educated, intelligent, and even scientifically-minded astrologers. We're not all middle aged women wearing turbans and shawls, sitting in foggy tents at the state fair. To a person we would rather cast a chart and give specific insights and advice than talk in vague, mysterious parables. We are not magicians or charlatans; we are professionals. No responsible astrologer will claim to know why or how astrology works in some scientific sense, but we have two millenia of study and data to draw upon, making the assertions of astrology far more than fantasy or whim.
I want to end by speaking to tusayan's post... Belief is a strange, strange thing. In the end, we are all constrained to believe - to take on faith - the vast majority of the information we use to live our lives. For some reason, we tend to get pretty worked up over metaphysical beliefs (God exists vs. God does not exist, or astrology works vs. astrology is baloney), which strikes me as silly. Immanuel Kant famously set out to prove that God existed, and managed only to prove that you cannot prove that God exists. Astrology, for all its tie-ins to the physical world, is a metaphysical (mythological) exercise, and no matter how intensely we may hold our metaphysical beliefs to be true (or our neighbor's to be wrong), we're not going to prove anything either way. Whoever speaks last, wins, as Kant said. Best, to my mind, to try out as many ideas as you can, and to learn from all of them. Especially the ideas that have been around for 2,000 years.