Well, Jewish holidays are a bit tricky, given that they don't follow that pesky upstart Gregorian calendar (upstart given that the year is 5763 according to the Jewish calendar).
First, all holidays really start at sundown the day before. For example Shabbat (the Jewish Sabbath) starts every friday night after sundown, and ends at Saturday's sundown.
Rosh Hashanah, the Jewish new year, is the 1st of Tishrei every year. This year it was September 7th.
Yom Kippur, our Day of Atonement, is the 10th of Tishrei (September 16th this year).
The week-long holiday of Sukkot, which celebrates the harvest, begins the 15th of Tishrei (Tishrei's a pretty big month for us). To celebrate this holiday we build an open-air hut and decorate it with gourds. Traditionally one is supposed to live there for the week...but I'm Reform, so we don't really do that.
Simchat Torah follows two days after the last day of Sukkot, and celebrates reaching the end of the Torah and starting the weekly readings over from Genesis.
The eight days of Channukah starts on the 25th of Kislev (this year November 30th), or again, the night before. A century after Alexander the Great croaked, Antiochus IV (another Greek) was in control of what is present-day Israel. Whereas previous hellenistic rulers let the Jews pretty much go on with their lives, Antiochus put a hellenistic priest in the Temple, sacrificed pigs on its altar, forbade practice of Judaism, and killed Jews. A revolt was led by Mattathias the Hasmonean and his son Judah Maccabee (a big, bad-ass Jewish hero) and they succeeded. When they retook the Temple, they only found enough oil to light the Temple's menorah (candelabrum) for one night. This sucked because the menorah was supposed to burn every night, throughout the night. Miraculously, the oil burned for eight nights, by which time they got more oil. In celebration of this miracle (the 8-day oil,
not the military victory, Jews don't celebrate violence), we light our own menorah during these eight days. The menorah actually holds nine candles, the center one is called the Shamus, and is used to light the other eight.
Tu B'Shevat (literally the 15th of Shevat), is the Jewish new year for trees. That sounds weird, but Western society has a new year for school and new fiscal years. This date is used to calculate the age of trees, as the Torah says one shouldn't eat the fruit of a tree during its first three years.
Purim is one of our most fun holidays, though hardly as important as some others. Basically it celebrates Esther's victory (diplomatic) over the king's (the Persian king was Esther's husband) advisor Haman, who wanted to wipe out the Jews, because Esther's uncle Mordecai refused to bow to Haman. We have a big, crazy carnival, lots of fun. It's the 15th of Adar (usually in March or there abouts).
Passover (Pesach) begins the 15th of Nissan (similarity to Japanese automobile manufacturer is purely coincidental). It celebrates the Exodus of the Hebrews from Egypt. The reason for the word "passover" is because God passed over the homes of Hebrews when he visited the tenth plague (slaying of the firstborn) upon Eqypt. This finally convinced the Pharoah to let the Hebrews go, though he changed his mind yet again and sent an army after them. They ended up dead in the Red Sea, after Moses stopped parting it. Because the Hebrews had to flee immediately, without even enough time to let their bread leaven (rise), we don't eat leavened bread during this holiday (a whole week). Passover is usually in April.
There are other holidays as well, but I'm getting tired of typing. The most important is Yom Kippur by far. Channukah is actually not that important, it just has the best PR given its proximity to Christmas. Gift-giving really shouldn't be a part of the holiday at all. To quote
www.jewfaq.org "It is bitterly ironic that this holiday, which has its roots in a revolution against assimilation and the suppression of Jewish religion, has become the most assimilated, secular holiday on our calendar."