I don't speak or read Greek, but I have read in several places that the Greek word for sin that is used in the New Testament is the same word that is used to describe what happens when an archer misses his mark with his arrow.
That is, when Jesus spoke of sin what he was getting at was instances where we were "missing the mark", that is falling short or misunderstanding things.
What is especially interesting about this is that our English word "sin" connotes morality. Sin is a MORAL affront to God. Whereas "missing the mark" implies something less, as if Jesus wanted to redefine sin in our minds as times when we fall short, or actions that arise out of our not understanding things correctly. It's interesting to note that while on the cross Jesus said, "Forgive them Father for they know not what they do".
If for no other reason than as a thought experiment I would suggest that Christians try for a week or so to replace in their thoughts the entire concept of "sin" (which connotes a moral affront to God) with "missing the mark". I believe this will go a long way toward freeing one from guilt, and helping one to more fully appreciate what Jesus' atonement means.
As a side note, I must confess that I also see that it is in the best interests of the organized "church" to continue attaching the idea of "moral failure" to the word sin. To a certain extent churches control their members by playing on their guilt and fear. We humans seem to be programmed to seek God and to seek reconciliation with our creator. So what better way to control and manipulate someone than to convince them that their actions make God mad at them? And so we are told that we are sinners and always will be - i.e. we are going to keep pissing God off for our entire lives. And so, to balance things out we better do what the church says, to get back on God's good side. If you really think this through you will see there is a certain, if unintentional, truth in this.
Anyway, for Christians I suggest thinking of your sins as missing the mark, and every time you think or read the word sin, substitute misunderstanding or missing the mark. And over time see what effect it has on your understanding of Jesus' message.