"Is it necessary for a Christian to repent of his/her sins to receive God's forgiveness?"
After much discerning prayer, research, and thought, I have figured out the answer to this question. The answer is no. It is not necessary to repent of one's sins to receive God's forgiveness. God forgives us our sins whether we repent or not. That's the reason He sent His son to us, because Christ died for us we are forgiven. He is the payment for our sins.
So if God forgives us no matter what, what is the point of repentence? Why do we have to say we're sorry and won't do it again if we're just going to be forgiven? Isn't it easier to just accept that we'll be forgiven and everything will be okay?
There seems to be a word missing here. That word is reconciliation. While God will forgive us for commiting sins, we cannot be reconciled to him without repentance. The best example of this formula for forgiveness is the story of the prodigal son. The father loves the son no matter what he does. When the son squanders his inheritance on women and booze, his father still loves him. We know this because the father gave his son his inheritance knowing full well what his youngest son would do with it. The son could have lived his entire life in this manner and his father would still love him and forgive him, but he did not go out to find him and bring him home. However, the son came back. He acknowledged his wrongdoings and expressed remorse over his actions. In return, his father prepared a feast for him and welcomed him back with open arms.
God loves us all, He forgives us because of His love for us. When we acknowledge that we have sinned, and promise to sin no more, He welcomes us home and prepares a feast for us. When we repent of our sins, not only are they forgiven but we are reconciled to God and can (by His will) enter the gates of Heaven.