Yes, jealousy is healthy to a relationship, but it should be in the right amount. By saying that, I mean that it should not be the kind of jealousy that makes you act crazy. Jealousy is a sign of loving your spouse such that you would love it if they were only yours and that you don't share him/her with another person. I am not saying that you should act possessive in a relationship, if you realize that your spouse is happy with another person, you should be happy for them. You cannot prevent becoming jealous, but you can learn to move on and let him/her be happy.
Extreme jealousy is a bad thing in a relationship. It is a sign of low self esteem and insecurity. No one would love to be in a relationship with someone who is not secure and does not know his/her worth.