What happens to people who have never heard of Jesus Christ?

I just found this clip of Oprah Winfrey asking essentially this question.

Do you think if you are somewhere on the planet and you never hear the name of Jesus but yet you live with a loving heart. You lived as Jesus would have had you to live. You lived for the same purpose that Jesus came to the planet, to teach us all. But you are in some remote part of the earth and you never heard the name of Jesus. You cannot get to heaven you think? ... Does God care about your heart or does God care that you called His Son Jesus?

There is an answer. From mormon.org here is an explanation.

Heavenly Father knew that many of His children would never have an opportunity to learn about Jesus Christ during their lives and that others would choose not to follow Him. Because He loves His children and is just, God provided a way for those in the spirit world to learn about His plan, have faith in Jesus Christ, and repent. Those who choose to accept and follow Jesus Christ will have peace and rest.

There is also a video from a member from London.