To answer the original post: Yes, I believe that everyone is savable. However, having said that, I don't believe that everyone WILL be saved.
First, relative to a large number of comments, I want to state that I am a Christian, however, I don't believe that the Bible is the ultimate authority - I believe that God is the ultimate authority.
Second, I also believe in continuing revelation and an open scriptural cannon - that is, I believe that God, who I view as a loving, Heavenly Father, continues to guide and direct individuals who seek his guidance. This guidance can be sought through prayer and meditation, and can be received as inspiration from the Holy Ghost.
Third, I believe that personal salvation is a combination of grace and works - that it is by grace that we are saved, after all we can do. Belief/knowledge that Christ is the Savior/Redeemer is not enough - "Thou believest there is one God; thou doest well: the devils also believe, and tremble. (James 2:19, KJV)" Accepting Christ is a necessary step to salvation, but if we do nothing more than acknowledge him than we have failed to understand our duty as Christians. I believe that at judgment day God intends to hold us accountable for our actions, relative the light and knowledge that we have.
So, a person who is simply told that Jesus is their Savior by a friend is different from a person who has received, through the Holy Ghost, a witness that Jesus is their Savior. In the first instance, that individual will likely be accountable for whether or not they sought out the truth of Christ being their Savior. In the second instance, that individual will likely be held to a higher standard, because of the revelation which he has received.
Unfortunately, as humans, we sometimes choose to go against what we know to be true/right. The ability to choose is the test of mortality - to see whether we will obey, or not. Those who have had much light and knowledge given to them, and then choose to turn away are held accountable for such actions. While it is possible for someone deep in sin to repent and change, it is often difficult, and some, lacking faith, choose to give in to their sins, rather than fight their way out. Thus, while they COULD have been saved, they choose not to be saved.
Finally, there are likely millions, perhaps billions, who have lived throughout the history of the Earth, who never had the chance to even hear the name of Jesus Christ. My beliefs are that the spirit of each person, when they die, goes to a place of waiting. There, those who know the truth have the opportunity to teach it to those who do not:
"For Christ also hath once suffered for sins, the just for the unjust, that he might bring us to God, being put to death in the flesh, but quickened by the Spirit: By which also he went and preached unto the spirits in prison;" (1 Peter 3:18-19, KJV)
"For for this cause was the gospel preached also to them that are dead, that they might be judged according to men in the flesh, but live according to God in the spirit." (1 Peter 4:6, KJV)
Thus, those who never had the opportunity in mortality to accept Christ are given the choice, for which they can now be held accountable.
I realize that some of the ideas presented here are not widely-held beliefs. The scriptures offered are humbly submitted for support. If you have a differing opinion, I welcome discussion, and, of course, encourage you to go directly to the source - ask God for yourself and see if you can confirm or deny my beliefs, by citing the ULTIMATE authority.
