The desire for revenge seems to be a cultural norm for some people--that's just the way things are done, especially in may of the micro-cultures of the world.  Males seem to be particularly vulnerable to the desire for revenge, but women aren't immune from its bite.  The desire for revenge is the desire to "get even," as if repaying injustice for injustice is somehow evening scales.  It almost always ends up hurting someone, usually in unforeseen ways.

First off, the desire for revenge is in many ways an obsession.  Obsessions always pull our focus away from more important aspects of our lives, such as family, friends, work, and enjoyment of all that we have.  Obsessions prevent us from being present in the moments in which we're living.  If we're so caught up in thinking about this something that someone has done to us, so caught up in thinking about how we're going to get back at that person, we can't concentrate fully on any task at hand.  How can we get the most out of any given day if we're thinking the entire day about something negative that was done to us and how we're going to commit some sort of negative act against someone else?

Second, taking revenge always brings us down a few notches.  We lower ourselves to a level at which it's often difficult to respect ourselves, and our self-esteem and self-image suffer, sometimes unconsciously, but always to some extent.  If the act that was done to us was low enough to upset us, the act that has to be done to exact revenge has to be just as low.  If we disrespect the person who hurt us, how can we respect ourselves if we do something just as low?  We may feel the momentary thrill of self-righteous "getting even," but in the long run, we've diminished ourselves and who we are.

Third, as Francis Bacon notes below, people who focus on revenge don't allow the hurts of a transgression to heal--they keep the wound open by focusing strongly on it, by making it a focal point of their lives, and they think that the moment of revenge will cause it to heal instantaneously.  They're wrong.  The only way those wounds will heal is through forgiveness--revenge is merely a momentary painkiller, but the hurt remains.  And it's not a painkiller that one can take over and over, either.  It's a one-time shot that wears off quickly.

People I've known who focus on revenge tend to lose much of what the world offers them.  They don't see the beauty around them, and they don't even consider the potential benefits of forgiving whatever transgression has occurred.  Worse still, people who have gotten their revenge find in retrospect that it wasn't nearly as sweet as it seemed it would be.  They find that most people don't share in their glee at having harmed someone else, and they even find that they feel a bit bad for that someone else.

I've been in the situation myself, but I've been fortunate enough to learn rather early on that revenge accomplishes almost nothing constructive in my life.  So I "get back" at someone--big deal.  It hasn't made me a better person, and it hasn't improved my relationship with the world; in fact, I've harmed the world by adding to the discord and anger of the world, rather than adding to the harmony and peace of the world.  Every action we commit adds to one or the other, and I don't want to be adding any more harm or anger--there's enough of that as there is.

If you really need to take revenge on someone, then by all means, do so--nobody's going to be able to convince you that it's wrong to do so.  But please consider the alternative that will help you to grow as a human being and will help you to have greater peace of mind and a stronger presence in the moment.  Forgiveness is much stronger than revenge, in all possible ways.