Science Fact: Men and women get jealous over the opposite things, and react to those things on a subconscious level.
Scenario 1: You are happily dating your girlfriend, Janey McGirlfriend. You are entirely devoted to her, but part of you believes you might be developing serious feelings for her friend, Batgirl. You never act on your feelings, of course, but one afternoon you decide to share your attraction troubles with a close friend. "NOOOO," cries your girlfriend, bursting out from under a nearby manhole cover and clambering onto the street. Everyone stares at each other for an uncomfortable moment. "NOOOOOO," your girlfriend reiterates, fleeing down the sidewalk and out of your life forever.
Scenario 2: In a very complicated situation, you accidentally have intense physical relations with Batgirl, due to a supervillain. You don't like her or anything, though. Overcome with guilt, you tell your girlfriend about it, certain that she is going to punch you over and over until you are dead. All she does is hug you and then buy you your favorite kind of cake (the kind shaped like a rocketship). Everybody is happy.
"Cheating" means a very specific things, to guys: it means that pants came off and biology happened, or at least mouths interacted in a way that did not involve a hotly contested sandwich. To guys, if you didn't do anything, then nothing happened, and that is the end of that. But jealousy works differently for both genders, and in a way that is actually very sensible.
The Science: A 1992 study illustrated that, in relationships, men are mostly afraid of their partners engaging in the physical kind of infidelity, but that prospect bothers women less than emotional infidelity. And of course you can't just ask people what scares them in relationships, because people are unreliable, and will probably just say "Ummmm, tarantulas." So this experiment involved all kinds of Science Machines that monitored skin conductance, facial electromyography, and brain angriness. The point is that these were immediate, physical responses—largely uncontrollable, and certainly not informed by logic.
The evolutionary reason for all of this, according to the awesomely named Doctor Gad Saad, is that our caveman ancestors needed caveladies to bear children—their children, not the children of some cave-player with a backwards hat who drove his own triceratops. In other words, sexual infidelity scares guys the most because only guys are able to wonder whether or not they're the father. Meanwhile, caveladies needed providers, because you can't bludgeon a woolly mammoth with a rock and keep a baby alive at the same time. So for them, emotional infidelity would be worse—a meaningless fling with a cave-trollop would ultimately be less threatening than a loss of dedication, or the possibility that the guy would stop bringing home the bacon. Uh, cave-bacon.
Now, this is all just a theory, and many people consider evolutionary psychology a special kind of crazy moon science, so you can take it or leave it. But the part about the jealousy differences is less crazy, and gets demonstrated again and again and again.
So What Should I Do About It?
All you really can do is be aware of how jealousy affects other people who are not you. Remember those immediate physiological responses we brought up? Well, imagine that you walked in on Janey McGirlfriend engaged in nude shenanigans with your worst enemy, Eric... um, Eric Dracula. That sinking feeling in your gut? The cold shock washing over you? That's the sensation women feel over emotional infidelity. Or in this case, vampirism.
This same principle may work in other situations. For example, is flirting while in a relationship totally harmless if there are no emotional attachment involved? Or is it totally harmful, in that seeing your girlfriend flirt makes you repeatedly harm the wall with your face, in a jealous rage? There's no actual answer to this, because it depends on how both people in a relationship feel about it; there are more reactions than your own to any given situation, so you'll find relationships a lot easier if you make an effort to look at all this stuff from the opposite perspective.