The primary verses in question is John 20.22-23, which read: "And when he had said this, he breathed on [the disciples], and said to them, 'Receive the Holy Spirit. If you forgive the sins of any, they are forgiven; if you retain the sins of any, they are retained.'"
Actually, this is a rather difficult question for us Protestants, because believe it or not, the Roman Catholics have not only this and several other verses to back up their claim, but they have over 1,800 years of written tradition supporting the contention that the Church has the authority to forgive sins in the name of Jesus.
In the New Testament there are at least three times where we read about making confession for our sins. James 5.16 demands that we "confess our sins to one another," thus there is a precedence, yea a command, to make confession.
Then there are two other passages from the mouth of Jesus himself regarding the forgiveness of sins: the verses cited above from John and Matthew 16.19 where Jesus spoke to Peter, "I will give you the keys of the kingdom of heaven, and whatever you bind on earth shall be bound in heaven, and whatever you loose on earth shall be loosed in heaven." Although some have argued that this passage does not refer to forgiveness, there is really no good reason to suggest that, especially when comparing this verse to the content and form of John 20.22-23.
There is yet more evidence to suggest the Catholic Church has put a right interpretation on the Church's authority to proffer forgiveness in the name of Jesus. From the earliest extra-biblical writings of the early Church leaders, we read that the practice of confession and forgiveness was not only an accepted practice, but that it was the norm. One of the earliest references we have is found in a letter from Clement to the Corinthian church, written near the end of the first century. There he urged them not only to confess their sins, but to "submit themselves to the presbyters and receive correction so as to repent." And before 236 we know that the practice of the priesthood conveying forgiveness had become standard because of the writings of Hippolytus, writings which are accepted as authentic by virtually all scholars.
So, for at least 1,800 years the Church has been pronouncing the forgiveness of sins, and Jesus on two occasions makes it plain that his followers do just this. So, when Martin Luther posted his objections to the Catholic Church's practices in 1517 thus starting the Protestant Reformation, why did the practice of confession and penance come to an end?
Because of the abuse of power by the Roman Catholic Church to provide forgiveness to the wealthy for compensation. Luther recognized these abuses and objected not only to the abuse of power, but to the rite of confession and penance. And thus came the fall of the practice.
So, is forgiveness in the hands of the Church?
There are indeed verses that place the act of confession and forgiveness not in the hands of the priests, but in the presence of Jesus. The first indication we have that the exclusive authority of the priesthood to forgive sins has ended is seen in the moments after Jesus' ultimate sacrifice and death. In the gospel of Mark we read, "And the curtain of the temple was torn in two, from top to bottom" (Mark 15.38). The temple curtain separated the ark of the covenant from the people and represented the exclusive authority of the priesthood to make atonement for the sins of the people. However, its tearing from top to bottom indicates that God opened the doors to forgiveness to all without the intercessory priest.
The letter to the Hebrews is probably the most damaging to the exclusive rights of the priesthood to offer forgiveness. In Hebrews we read that Jesus himself has usurped the authority of the priesthood to make forgiveness and that we, as followers of Jesus, have the right to come to him directly to offer our confession and receive forgiveness (Hebrews 9). Thus there is ample evidence to offer that those seeking to be forgiven of their sins need not prevail themselves upon the Church to receive that forgiveness. On the other hand, there also seems to be little evidence that the Church doesn't also have the authority to forgive in the name of Jesus.But contrary to recent pronouncements, the authority of the Church isn't limited to just one "brand" of the Church, and so the authority to forgive sins in the name of Jesus transcends the exclusive claim of the Roman Catholic Church.