Forgiveness is one of the most wonderful gifts to receive, but yet one of the most difficult to give. In the event of an argument, the "offender" can nearly always be heard to say something along the lines of, "Can you ever forgive me?" Children who fight tend to say things like," I'll never forgive them!" When someone truly hurts you, you wonder if you'll ever be able to look at that person again without recalling the pain they caused you. Real forgiveness, without grudges, is much sought-after.
Then we have those who say, "Don't worry about it! Forgive and forget! It'll be like it never happened." I see a real problem with this line of thought: if you forget the issue, you'll never learn from it. The one who made the mistake needs to suffer the consequences of their actions in order to avoid repeating it, and the one who was hurt should deal with their pain, rather than pushing it aside for the sake of ending an argument (or any other reason).
If you forget something ever happened, you forget the mistakes you made, and you're therefore more likely to make them again. How can you learn if you forget? Both parties should remember what happened, however unpleasant, because then they'll also remember the steps they took to heal afterwards. Without conflict and reconciliation, there is no growth. Arguing and solving the problem brings people closer, because of what they've gone through together.
So forgive freely (and hold no grudges), but never forget.