A few months ago, I got dumped by a girl I had been dating for a while. Epically dumped, I would say—the complete story is something for another time. At any rate, within a week, I was pretty much over it. I wasn't angry anymore, and pretty much had already forgiven her for what she did to me. Some of my friends started asking me, "Why are you doing that, after all she did to you?"
But I'm all about forgiving people. And my gold standard for that is John Paul II.
In 1981, while in St. Peter's Square, he was shot four times by a Turkish sniper named Mehmet Ali Ağca. The Pope lost three quarters of his blood, and was in surgery for five hours afterward. Not only did he forgive his attacker, but he met with Agca in prison, and later met with his family. In June 2000, he got Italy's president to release Agca from prison, where we was extradited to his native Turkey to serve out a previous prison sentence.
This idea of forgiveness, of course, has deep roots in Christianity. In the gospels, Peter (the apostle I consider to have gotten his name because he is dumb as a rock) approaches Jesus and asks, "How many times should I forgive my brother? Seven times?" And Jesus replies, "I say to you, not seven times, but seventy times seven." Which may have been to say, forgive him until you have lost count, and then keep on forgiving him.
He then goes on to tell a parable to illustrate this point (which you can read at that link—it's difficult to summarize). His point at the end is that, since all of us do something wrong from time to time, we do not deserve God's forgiveness unless we are willing to show forgiveness to the people in our lives. This is the source of the line in the Lord's Prayer that goes, "Forgive us our trespasses, as we forgive those who trespass against us."
You may respond here, "But I don't believe in God, and I am pretty sure that you don't either. Why would I need the forgiveness of someone I don't believe in?" To which I say, "You're missing the fucking point."
The benefit of forgiving people is not in what you do for the person who is forgiven, nor does it have anything to do with the extrinsic benefit you might gain in the Kingdom of Heaven or what have you. The benefit is that it makes you a better person. When you hold a grudge against someone, the emotions are all negative. You give yourself a justification for being angry and hateful. On the other hand, forgiveness is an act of empathy and understanding, to try to consider why a person would make the kind of mistake that they did. Above all, though it is an act of love, the basic kind of love that one extends to everyone just by virtue of being human. You know, the kind of love that makes us concerned about people in poverty- and disaster-stricken areas, even though we have never met these people.
That doesn't mean, of course, that we should let people walk all over us, and treat us like doormats. Generally speaking, a lot of the ways that people hurt us come about only because of a certain amount of trust we put in them. That trust can be taken away if they misuse it and violate it. If they continue to do you wrong, you can completely cut them out of your life, but I don't think there ever comes a point where you should stop forgiving them.
To relate this back to my personal life, I forgave my ex only days after she dumped me. I was still hurt and upset, of course, and I was still processing the experience in my head. And forgiving her didn't mean I would immediately take her back if she wanted to start dating again some months down the road. I sort of consider her a friend, but right now she is just "a girl I know on the internet," which is the very bottom of the friend hierarchy. But on some level, I still think of her as a friend.
"So, Tim, why you gotta forgive?" "That's just how I roll."