When somebody wrongs you, can you forgive them if they do not want to be forgiven?

Forgiveness is a relationship that fosters healing; it is not ignoring harm someone has done to you, it is not laughing it off, nor is it "getting over it."

I struggle from time to time, as we all do I think, with what to do about the harm others have done me. Most of the time, I have just laughed it off, sometimes I've chosen to ignore it, and other times I've just gotten over it with time.

I have come to a point in my life where most of the time I just let go of the pain and anger I feel toward those that hurt me. Rather than continuing to agonize over the offenses of others I try to remember that our Savior said to forgive them"70 times 7".
The number seven is symbolically the perfect number or the number that symbolizes God. Therefore in symbolic language of course the Savior meant seventy times seven as the perfect number to the tenth, times the perfect number. I'm no scholar, but I think the meaning is obvious; forgiveness is required of us always. In my experience it is that first time that is the hardest…LOL

What of the ones that hurt us and never ask to be forgiven? I'm not sure, but I think that the Lord is requiring of us, note I did not say asking of us, to be ready to forgive always.
Forgiveness is an active thing, it is a relationship, a process through which healing of a broken trust is restored. It therefore stands to reason that it requires both parties to be actively involved. For example, when two nations go to war, the war does not end because one of the nation says, "wait, I forgive you" and packs their bags to go home. Hurt feelings and major wrongs likewise are not able to be forgiven in such a one sided way. Therefore, while one person may want to forgive, there are limits to how far they can do so without both parties being involved.
This holds true in the gift of the atonement. Our Savior has already paid the price of our sins, but that debt goes unpaid until we ourselves decide to accept the gift. We must humble ourselves to him and take his offered forgiveness; otherwise it is wasted and we remain alone and unforgiven.
In this process of forgiveness both parties must be willing to not only forgive, but to be forgiven. How often do we hear of someone saying, "sure I can forgive him/her, but I did nothing wrong." It is possible to have no fault in the starting of an argument, but once it has begun is it possible to have done nothing wrong or to have caused no offense? Taking part in an argument with your brother, even when you were "only defending yourself", implies a certain level of culpability. Further for the process to work a certain amount of humility on the part of both parties is necessary.

Humility is necessary for true forgiveness to take place. Both the one who gave offence and the one that was offended must understand that they are both subservient to the Father. Our Father in Heaven wants us to reconcile and become one again; he does not desire one to lord over the other or to use the offense as a tool to hurt or hold claim over the other. Showing humility to one another both in contrition and in forgiveness does not just show respect for one another, but our true love of the Father.
God's instructions are plain and easy to understand if we truly put his will before our own. He does not require more than we can do, nor things that are not possible. It therefore stands to reason that our Father could not have demanded of us to be perfect in our forgiveness but rather to be perfect in our willingness to forgive. For while we can not change the hearts of others and make them humble and contrite, we must needs be humble in our own hearts and willing to forgive those that have hurt us even if we are unaware of what on our part has caused hurt in others.
Likewise it is important for us, as we attempt to forgive others, to remember that the old adage “It is easier to give than to receive” is even more true when it comes to forgiveness. How much easier is it for you to forgive the hurtful words, said in the heat of anger, by your spouse than it is for her to humble herself to ask for that forgiveness; or often just as difficult to accept when offered without being asked for.
The human spirit can be a vain and spiteful thing; it is only through our humility and by following the loving example of the Savoir that we are able to over come our natural selves and allow forgiveness to work in our lives.