While I am Jewish, from what I have learned about other religions, I would have to say that tradition is no more or less important to the Jewish religion than it is to any others. Certainly, all forms of Christianity have important traditions, as do Muslims, Hindus, Sikhs, and so on. However, historically, Judaism has probably experienced more discrimination than other religions, in most of the countries in which it has been practiced. Sadly, there continues to be evidence of this to this day. I think that this has a way of making many Jewish people feel they have to make a strong point about religion, emphasizing the traditions to show that no matter what, Judaism will be carried on. Additionally, there were any number of societies in which Jewish people had to practice their rituals secretly, for example, during the time of the Spanish Inquisition. So, today, where in many countries Jewish people can be open about their Judaism, they are so happy about this it probably seems like tradition is more important than in other religions.
Tradition is important to Judaism for a number of different reasons. First the Old Testament contains many laws, especially within the Pentateuch. There are laws for everything from how to worship, to work, and even about which types of clothing can be worn and what types of food can be eaten. If you read the narrative of the Old Testament you can see that time and again the people of Israel are punished by God for breaking the laws that He has set out for them. By the end of the Old Testament (chronologically) the nation of Israel (the northern 10 tribes) are first taken into captivity by the Assyrians and later the nation of Judah (the southern 2 tribes) are taken into captivity first by Babylon, then Persia, then the Greeks, and finally just before the time of Jesus the Romans take control of the Holy Land. During this time Jews saw their captivity as punishment from God. Because of this they began to follow strict adherence to the Law of God, in order to show that they were not like the past generations who disregarded the Law. Jews follow tradition strictly because this is what their religion is about. Their strict adherence to tradition may be further intensified due to the fact that there are no priests and so there are no sacrifices being made for the sins of the Jewish people.
Tradition is very important to Judaism. Much of the Jewish religion centers on tradition. People are supposed to pray three times a day. The prayer times are fixed times based on the rising and the setting of the sun. There are certain practices that occur each week that are part of the Jewish tradition. Observing the Sabbath, lighting the Sabbath candles, blessing the wine, having a Sabbath meal, and blessing the children are all part of the traditions of the Sabbath. There are certain greetings and phrases that are used to convey meaning for Jewish people. At this time of the year, these greetings are about having a happy new year and being granted another year of life. There are lifecycle traditions that also are part of Judaism. At Jewish weddings, a glass is broken to remember the suffering the Jewish people have faced throughout history. The bride and groom are married under a chupah. For Jewish teens, they have a bar or bat mitzvah that signifies their passage into Jewish adulthood with Jewish, adult responsibilities. There are traditions associated with mourning. Sitting shiva is a custom of mourning that allows for people to console somebody who has lost a loved one. There are traditions associated with dietary laws of the religion. Being Jewish means observing traditions in almost every aspect of life.