Like any serious question in Judaism, there is a Machloket.
The Gmara clearly believes in astrology and that many thing are an affect of a mans Mazal.
אמר רבא חיי בני ומזוני לא בזכותא תליא מילתא אלא במזלא תליא מילתא
(Moed Katan 28a) This include חיי בני ומזוני, how many years a man will live, how many children will he have, and how much money. Yet there is a Machloket (shabbat 156a) if יש מזל לישראל or not.
Most of the Rishonim and Achronim agree that astrology is an integral part of Judiasm. But they disagree if אין מזל לישראל means that they are completely unaffected by astrology or rather thay too are affected, but that they can use prayer to change their Mazal. See Abarbanels commentary on Deut. 4. And the Mepharshim on shabbat 156a-b.
As with many mystic believes, the Rambam did not believe or support the idea of astrology in Judaism. In a famous letter to the sages of מארשילייא the Rambam called astrology "beliefs of the fools" and claimed that we have no obligation to believe in it, since only a Daat Yechid speaks of it in the Gmara, and philosophy (science) has proven it to be nothing but superstition. Obviously, the Rambam was highly criticized for this, but never the less it is still a legitimate view.
When it comes to Halacha, it seems that the rule is that astrology is real, and that יש מזל לישראל. for an example to this, the Halacha is that a woman that two of her husbands died (even if not from a natural cause) cannot remarry since we say that her Mazal caused her husband's to die. Here is the Pask of a Biet Deen in Israel.