Are You Supposed to Fear God?

The following answer comes from www.chabad.org.

Question:
What's all this business about being "G‑d fearing"? What are we supposed to be afraid of?
Answer:
When we say that a person is "G‑d fearing", we don't mean he or she lives in fear that G‑d might punch them out for doing the wrong thing. The term for that would be "fear of punishment" (if a great big monster in the sky would be threatening the same, the fear would be the same, right?).

Of course, it's better to do the right thing because one is afraid of punishment than to kill, steal and cheat because the policeman isn't looking and one doesn't believe in a Higher Authority to whom man is answerable for his actions. Still, righteousness that is motivated by fear of punishment does not represent a very high spiritual or moral state of existence.

The Chassidic masters explain the true meaning of "G‑d fearing" as a fear of separation from G‑d. Like a child who is afraid of being left alone by its mother. So, too, a healthy soul will recoil from certain actions out of the awareness that these actions will place a barrier between herself and her Beloved, between the "spark of G‑dliness" it embodies and its Source.