We believe that men will be punished for their own sins, and not for Adam's transgression. - Second Article of Faith, LDS
I know what you're thinking: "so what?" This was a big deal at one time and has caused many arguments and discussions through the ages. I want to define a couple of terms first:
Sin - To act knowingly or willingly against the will of God. So it's wrong, you know it's wrong and your gonna do it anyway. Sure you might rationalize it somehow, but it is still wrong. That is sin, got it.
Transgression - To act against the will of God. You don't know it's wrong, it is and you are doing it. You'll find out later that you messed up, but for now you are completely ignorant.
Ok, back to the the thing at the top. Back in the second century Irenaeus, the Bishop of Lion, came up with the doctrine of Original Sin. This is the belief that we all are born with sin because Adam was kicked out of the Garden of Eden. So that means a 1 minute old infant has sin or in other words has acted knowingly and willingly against the will of God. Bad baby.
This doctrine was not fully realized until the Catholic Church adopted the doctrine of infant baptism around the fourth century. So with this ammunition they taught that babies will go to hell if they are not baptized.
This doctrine was brought into debate during both the First and the Second Great Awakening (during which Christ's Church was restored) making this a very important topic for the last 300 years or so. This is why we felt it necessary to put this in our beliefs.
What we believe is that Adam Transgressed the law. God clearly stated: "thou shalt not eat [or] thou shalt surely die." -Gen 2:17. Meaning that if he ate the fruit he would die. He succumbed to another definition of dying, separation. He was separated from God by being kicked out of the garden. As a result all of us are not in the garden and not with God (eg. fallen), but we are not going to hell.
How is that you ask? We also believe in the innocence of little children. Since they cannot fully understand the laws of God, they cannot act knowingly or willingly against it and therefore are without sin. When they are sufficiently able to make these choices they are capable of sin and need the redemptive power of Christ.
So, we will all be punished for our own sins and not for Adam's transgression. So to sum up there is the Catholic view and our view:
Catholic - Adam sinned by partaking of the fruit so we all have sin and need to be baptized so we don't go to hell.
Mormon - We are not in the garden and are responsible for our actions.
I think it was best said: "Adam fell that men might be and men are that they might have joy."