Humans and other primates display jealousy - it appears to be an expressed phenotype - we will most likely know just how powerful this feeling/behavior is - we have a pretty good idea as to why evolution selected it to survive - it serves a purpose in mating fidelity (evolution is all about selecting genes that are advantageous to reproduction and offspring care - although we have regularly seen aberrations to this selection). In non-scientific terms - it's hard wired into human brains - to varying degrees - and given contributing factors in how you were raised (especially how your parents inter-related and parent-child and sibling-sibling behaviors) - you can find out, in your own personal history, just how much power "the green monster" can potentially have over you. As other posters here have noted - once jealousy overwhelms your daily functioning - becoming prolonged - you are now moving out of what nature designed and more toward mental illness.
A small amount is natural but if your jealousy is consuming all your daily thoughts, then no it's not healthy. Stalking your x is a chronic form of jealousy. If you can't reasonably or totaly believe in or trust someone then that person isn't worthy of your love or friendship. If you are secure in your own self esteem & worth as a person then this usually isn't a problem. If the person you put your trust in is not trustworthy then you know what you have to do if you have any self respect. People don't change drastically. They may hide things & then you discover the real them. That is often the case. Often with Jealousy comes the need to control the other person. Toxic relationships are not good for either person. Some people just can't settle for one partner to fill all their relationship needs. These are the players of life. I tend to steer clear of these types as partner material.