Answer: The evil eye is definitely a Jewish concept and not just superstition. The Torah relates that when there was a famine in the land of Israel, Jacob sent his ten sons to Egypt to get provisions. Because all of the brothers were strong and handsome men, Jacob was concerned that they would attract much attention and envy so he instructed them to enter Egypt from different gates and thus remain inconspicuous. Our Rabbis call this concern that Jacob had - "fear of the evil eye".
Jacob understood that G-d had blessed him greatly by giving him ten wonderful sons but he also realized that if he were to be insensitive and flaunt his blessings, it could cause great pain to others less fortunate than him. He was grateful for the blessings he had been given and did not want G-d to re-evaluate his eligibility for those blessings by letting them be a cause of anguish to others. It was this "evil eye" that Jacob wanted to prevent.
Based on the model set by Jacob, the Talmud teaches that one can easily avoid the "evil eye" by simply being sensitive to the feelings of others by being modest and not flaunting what one has. For example, our sages advise not to buy a field near the entrance to a city or in any other very public location as the sight of a plentiful field can evoke painful feelings for those less fortunate. A real halachic expression of this concern is the custom not to call up a father and son or two brothers, one after the other to the Torah reading. So too, one may not give the same name to two children in the same family. The reason for these laws are the same as above - in order not to draw too much attention to oneself and being aware of the feelings of others who may not be in such a fortunate position.
For those really concerned about the evil eye there are many "antidotes" such as tying red strings around one's wrist or the Hamsa ("Five -Fingers") symbol. But one should always ensure that the antidote used is authentic and one commonly used by Jews as there are many floating around these days that are based on witchcraft.
However, the best approach to the evil eye is that offered by the Talmud - "one need not be overly particular but one should be mindful". This means that one need not carry all sorts of amulets and antidote material but one needs to be mindful of the evil eye by behaving modestly and with a genuine concern for the feelings of others.