It depends on the person whether religion is important in one's life. Religion plays a key role in many people’s lives, and almost no part in others. However we all need to be sensitive to religions and religious differences, so religion is important to everyone.
Psychologically, I think religion provides answers to questions (death, justice, etc.) that would otherwise be unanswerable. Perhaps not as many, or as clear-cut as we'd like, but answers nonetheless. Sociologically, as others have said, I think it gives us community, and fulfills our need to have other people around us with a common set of beliefs. This can have rather ugly consequences, but it doesn't necessarily have to be that way.
The word "religion" is derived from a Latin term that implies a binding together. One function that religion has often served in society is to bind members of society together through a shared set of values and goals. Unfortunately, religion has also sometimes had the effect of causing great conflict, especially when two different religions come into competition with one another.
This is a question that only individuals can answer for themselves. The importance of religion is simply what one makes of it in their own life. For some, religion is very important. For others, it holds no power (or importance) for them. No universal answer can ever be given, or accepted, upon the importance of religion in life.
In Judaism, there is an emphasis on ethical behavior, in one's personal relationships, one's business dealings, and one's care for the world. In short, people are supposed to behave here and now, not because there is meant to be some reward or punishment in the future. This does not appear to make Jewish people any better behaved than anyone else, but personally, I do like the emphasis on behavior, as opposed to belief.
This is a question that will be answered differently by many people. Let me give you an answer from a Christian perspective. Many Christians would say that their faith give them meaning (as post 2 states), but they would also say that their faith gives them strength, the ability to love, the motivation to forgive, and the courage to press on. Many Christians would say that all of these flow from experiencing the love of God in Christ.
That depends on who you are. For many people in the West, religion plays very little role. However, if you are a religious person, then religion can give you such things as a sense of purpose (for example, that you are on Earth to serve God) and a set of values (whatever your religion specifies) to live by.