The number one reason may be that God requires it. (Please, read all the scriptures completely. Some May be fairly similar, but they have their own nuances and wisdom to bestow.)
Matt. 6:14-15
14 For if ye forgive men their trespasses, your heavenly Father will also forgive you:
15 But if ye forgive not men their trespasses, neither will your Father forgive your trespasses.
Matt. 18:34-35
34 And his lord was wroth, and delivered him to the tormentors, till he should pay all that was due unto him.
35 So likewise shall my heavenly Father do also unto you, if ye from your hearts forgive not every one his brother their trespasses.
Luke 6:37-38
37 Judge not, and ye shall not be judged: condemn not, and ye shall not be condemned: forgive, and ye shall be forgiven:
38 Give, and it shall be given unto you; good measure, pressed down, and shaken together, and running over, shall men give into your bosom. For with the same measure that ye mete withal it shall be measured to you again.
Luke 17:3-4
3 Take heed to yourselves: If thy brother trespass against thee, rebuke him; and if he repent, forgive him.
4 And if he trespass against thee seven times in a day, and seven times in a day turn again to thee, saying, I repent; thou shalt forgive him.
Ephesians 4:31-32
31 Let all bitterness, and wrath, and anger, and clamour, and evil speaking, be put away from you, with all malice:
32 And be ye kind one to another, tenderhearted, forgiving one another, even as God for Christ's sake hath forgiven you.
Colossians 3:12-14
12 Put on therefore, as the elect of God, holy and beloved, bowels of mercies, kindness, humbleness of mind, meekness, longsuffering;
13 Forbearing one another, and forgiving one another, if any man have a quarrel against any: even as Christ forgave you, so also do ye.
14 And above all these things put on charity, which is the bond of perfectness.
Mosiah 26:31
31 And ye shall also forgive one another your trespasses; for verily I say unto you, he that forgiveth not his neighbor’s trespasses when he says that he repents, the same hath brought himself under condemnation.
Doctrine and Covenants 64:10
10 I, the Lord, will forgive whom I will forgive, but of you it is required to forgive all men.

From these scriptures, it is pretty obvious that we must forgive if we expect to be forgiven by God. What is even more interesting, is the following scripture:
Matt. 18: 21-22
21 Then came Peter to him, and said, Lord, how oft shall my brother sin against me, and I forgive him? till seven times?
22 Jesus saith unto him, I say not unto thee, Until seven times: but, Until seventy times seven.
What is so interesting is the special meaning the number 7 can have in Israelite culture and language. The number seven can mean the quantity 7, or it can be used as the number of completeness. Basically, if this magic 7 is in use any this scripture or the few given before it, it means that even if someone sins against you completely, 70 times in a day, you must forgive them completely every time.

Your forgiveness may also help another repent, do better, and find joy and happiness in Christ more completely. This is what Paul taught to the Corinthians.
2 Corinthians 2:7-8,10
7 So that contrariwise ye ought rather to forgive him, and comfort him, lest perhaps such a one should be swallowed up with overmuch sorrow.
8 Wherefore I beseech you that ye would confirm your love toward him.
10 To whom ye forgive any thing, I forgive also: for if I forgave any thing, to whom I forgave it, for your sakes forgave I it in the person of Christ;

The person who did wrong toward you may, or may not, know what they have done. They may have also done it in innocence or ignorance. Because of these uncertainties, it may not be their problem. Even if it is, through malice or through the negative reactions in their lives, why make it your problem?

According to the scriptures in the above section, if you fail to forgive another, judgment will be upon you when God renders his judgments. This will be no fun... to spend all eternity in misery because you failed to let another have their own problems.

More immediate, and maybe more practical is how it affects you here and now. Think about it, when you are holding a grudge, you are less happy. Things that usually bring you happiness don't or else the happiness is shorter lived. You are more likely to be angry with anyone, including yourself. Depending on how heavy the grudge and the burden of carrying it, you may have noticed it can cause some back pain or other physical problems. At least, this is what I have noticed in my own life, and those of people I am close to.

For your own sake, forgive others. Find happiness in this life and the next, instead of the frustration, misery, and possibly pain that not forgiving can bring and/or cause.

Yes, this wisdom, if you will, was hard won. I am still struggling to fully live what I am sharing here. However, as I said, from personal experience, I know for a fact that not forgiving causes the problems I mention above.

If this isn't one of "the seven million dollar questions," I don't know what is. This one is rather difficult. So, to begin with, what does forgiving another entail? Well, I figure it includes at least the following:

• Letting go
• Allow God to be the Judge
• Being Kind and Courteous
• Forgetting It Happened
• Speaking only good of the person

One way to allow God to be the judge and to let go is found in Doctrine and Covenants 64:11 "And ye ought to say in your hearts-let God judge between me and thee, and reward thee according to thy deeds." By letting God be the judge, we begin to let go of some of the negative and vindictive feelings. We also begin to seek less vengeance.

Sometimes, forgiveness comes easy. However, I have often found it very difficult to forgive when the trespass was extremely painful or large. It is at these times that I have begun to realize that being able to forgive is a gift of the Spirit. I have found that sometimes, the only way I can forgive, is to pray for the other person. I also pray for the ability, strength, and desire to forgive the trespasser. I believe this may be the reason behind Matt 5:44 "But I say unto you, Love your enemies, bless them that curse you, do good to them that hate you, and pray for them which despitefully use you, and persecute you;"

How can those feelings and actions coexist with anger, hate, and holding a grudge against the trespasser? I believe they can't. To forgive, work to love them, to understand them, and to see good in them. Forgiveness will happen as a matter of course when you do.