Why 9 Lights at Hanukkah?

חנוכה = Hanukkah, from חנוך = education, but also means dedication
חנוכיה = Hanukkiah (9 branch candle-holder used only at Hanukkah)
8 lights represent the miracle for 8 days in which oil reproduced itself
1 light is the 'shamash', the servant candle which lights the 8
Compared to:
מנורה = Menorah, the 7 branch candelabra which rested in the Beit Hamikdash (Holy Temple) & illuminated the inner sanctuary. It was lit with a special processed olive oil from the olive press. The Menorah, the olive and its oil are the symbols of present-day Israel: the olive branch represents the supernatural peace of Hashem which rests over the Jewish People; olives must endure the pressure of the olive press to become the purest olive oil, a reminder of the struggle for the Jews to survive their dispersion among the nations; and the Menorah represents the nation of Israel, a light among the nations. Yet, more than that, the light represents the illuminated face of Hashem upon His people, and the fulfillment of prophecy that He will return this people to their homeland from the 4 corners of the world, NOT for their sakes, BUT for His namesake!