It is my understanding that each of us will only be accountable for our own sins. Paul taught that For as in Adam all die, even so in Christ shall all be made alive. Because of the fall of Adam and Eve, spiritual and physical death came into the world. All of the effects of the fall are overcome in Christ's atonement. For small children, who are too young to accountably sin, that means that there is nothing separating them from God upon death. However, were it not for Christ's atonement, everyone would go to hell, including little children.
Now, why does everyone sin? Or as an alternate title, Wouldn't it have been nice if the fall had never happened? Well, let's think of things that don't sin first. Things that don't sin: on one level, things that aren't intelligent enough to make choices based on reason. For example, rocks, dust, trees, air, animals (including mice and dolphins

). On the other level, things that are perfect don't sin. I only know one thing that is perfect though, and that's God. So one way of looking at it is that we sin because we aren't gods. We aren't perfect.
How do we sin? We sin when our will is not aligned with God's will. If our will were 100% swallowed up in God's will 100% of the time for our entire life, then we would never sin. Only one person has succeeded at that. The rest of us are too prideful, to self-willed to be perfect. In fact, part of the reason we are here is to learn to humble ourselves, and to be able to say truthfully "Thy will, and not mine be done."
Is it the fall that makes us desire to have things our own way? I don't think so. I bet if any of us were in the same position as Adam or Eve, we would make the same choice that they did eventually. The reason is because pre-fall or post-fall, we are still selfwilled. Adam and Eve weren't perfect before they fell, they were just innocent. They hadn't committed any sins, but they hadn't done anything good either.
The fall was the first time on this earth that man had sinned, and that is why it is when sin was brought into the world. However, man had a sinful nature even before then. What they didn't have was an opportunity to choose to break the commandments.
Sometimes we think of the fall as a great tragedy. We think that if only they hadn't fallen, we would be living in heaven on earth right now. However, it was really a great blessing. Didy, this is why I think Seamusz was saying that "technically" it wasn't a sin. In fact, many places in the scriptures refer to it as a transgression. Either way, here's where that idea comes from. The fall was absolutely necessary and planned for. Satan tempted Eve to partake of the fruit because he didn't know the mind of God. If we look at the commandments that God gave Adam and Eve in the garden, partaking of the fruit was the only one they had the ability to break. It was the only choice they had in front of them. We might ask, why did God even put that dumb tree in the garden? If he hadn't that would have solved the whole problem, right?
God placed the tree in the garden for the same reason that Satan is still on the earth today. God created this earth to prove us, to see if we would obey his commandments. How could we obey his commandments willingly if there were no other choice? Opposition is necessary in all things. The only way we can exercise our free will, and show God that we love him and want to obey his commandments, is if there are other options which we find enticing. Satan tempts us all to satisfy our own desires rather than desiring to serve God. He entices us to choose that which is evil.
If it weren't for opposition in the world, ie if there had never been a fall, we couldn't be righteous, because we couldn't be wicked. We couldn't be happy, because we couldn't be miserable. We couldn't grow and learn, but would remain forever in the same state of neutrality, neither happy nor sad, neither righteous nor rebellious. This would frustrate the entire plan of God in testing us. He isn't just testing us either. If he just wanted to give out A's and F's there would be no point. He created this earth to give us an opportunity to progress, because he loves us. He wanted to give us the opportunity to grow and progress, to be able to become more like him. And he knew that the only environment where this progression would be possible was one where there was strong opposition, and we would be required to live by faith. God planned for the fall to happen. His foreknowledge of that act is the reason he prepared a Savior even before the foundations of the earth were laid. This is why some say the fall was only a half-sin or whatever. Because God needed it to happen to progress his other works. And no matter what we do, if we are doing God's will, we aren't sinning. (Don't twist that into thinking that anything we do is okay

)