Hanukkah is also known as the Feast of Dedication, or Feast of Lights. In John 10:22 we see Jesus in the temple during the Feast of Dedication, or Hanukkah. Along with the fact that Jesus was Jewish, I believe this is sufficient evidence to show that Jesus himself celebrated Hanukkah. Hanukkah is never said to be a required celebration for God's people, but we can see that God's people, and even Christ himself, celebrated this feast. We are called to be imitators of Christ and do the things that he did. This led me personally to desire to partake in this celebration. 

Hanukkah celebrates the cleansing and re dedication of the temple back to God. God preserved the Jewish people from their pagan enemies that persecuted them and sought to destroy the Jewish culture and people. But God had plans to bring forth the Messiah through the Jewish people, and therefore preserved them and conquered their enemies. The new covenant significance of Hanukkah is revealed in the fact that God's temple is no longer a building, but is within our bodies. Satan has sought to destroy the new covenant temple as well, but Christ cleanses our bodies and frees us from sin as we re dedicate our bodies and our lives to God, or back to God. The menorah lights have a new covenant significance in that Jesus is the light of the world and our lights shine when we allow God to live within us and lead our lives. Hanukkah also displays the sovereignty of God in that he always accomplishes his purposes. The miraculous power of God is also featured in Hanukkah in that the candles were allowed to remain lit for 8 days off of 1 days worth of oil. This allowed them enough time to acquire more oil before they ran out and this is also the reason why the Hanukkah celebration lasts for 8 days. So while Hanukkah doesn't appear to carry the same weight of importance as the other feast days of God, it does have significance and biblical support. It is also a good substitute for those that are breaking away from the traditions of Christmas. Hanukkah can fill the void that many will have from separating themselves from their old traditions of Christmas.