As one who comes from a Reformed understanding of the doctrines of grace and justification I do not agree with my Roman Catholic friends on many of their positions regarding the sacraments. For example I do not believe that the Church has the power of absolution of sins for the Church is only the body, but the prerogative and power to absolve sins is in Christ alone. Hebrews 7:24-25 says, "Jesus... because He continues forever, holds His priesthood permanently. Therefore He is able also to save forever those who draw near to God through Him, since He always lives to make intercession for them." Going to a priest to make confession has certain psychological benefit (as the Roman Catholics recognize) but should not be mistaken as providing a means for salvation. That said we Protestants tend to throw the baby out with the bath water. We get so nervous about doing something that is misunderstood that we don't do it at all- even when Scripture commands us to. James 5:16 says, "Confess your sins to one another, and pray for one another so that you may be healed. The effective prayer of a righteous man can accomplish much." This instruction is given in the context of the local church as James addresses the responsibilities of the elders (local church office) in the preceding verses.
Scripture teaches us that it is good to make confession to one another. We are all priests in this sense for one another (1 Peter 2:9 teaches that we are a kingdom of priests). We intercede for one another. This confessing to one another and prayer for one another is not for the absolution of sins. Christ accomplished that on the cross and through His resurrection from the dead. It is for our daily sanctification- submitting ourselves before God and repenting from sin. Confession is integral to our pursuit of repentance and confessing to others keeps us honest in that pursuit.
So why do we not practice confession to one another in the local church? We have become a privatized society. People drive home from work, pull into the garage, and never engage with their neighbors. Turn on the TV, hop on the internet, or start text messaging and you never really have to engage with your family either. A few years back I mentioned to another man (that I considered a spiritual leader) in the church where I was a member that I was concerned about a particular married couple in our church and their relationship. I felt we should go to the husband and offer help. His counsel was to mind my own business, "You don't bother another man's house." This really disappointed me and it continues to disappoint me how disconnected and privatized a church family can be. This is no different than the world. Confessing your sins to one another is not only a good habit to cultivate, but it is a command. It is a spiritual discipline. We need to invest in each other's live no matter how uncomfortable and awkward it makes us feel. This displays Christ! I'm not advocating having everyone stand before the congregation to air out everything but each believer should have other believers in their local church that they are accountable to and confess sins to. This is part of what it is to daily experience victory over sin and part of what it is to be in the family of God.