What about people who have never heard of Christ?
Another way this question is often phrased is, "What about the innocent natives in Africa?" The truth is, there are no innocent people. The Bible teaches that we are all imperfect, selfish, weak, sinful, rebellious, and spiritually unclean. We are all dead in our sins and deserving of God's wrath (Romans 3:9-20; Ephesians 2:1-10). (For a more thorough examination of this, see our Christian Cram Course.)
The Bible makes it clear that through nature and conscience each person has some knowledge about God and sin for which he is accountable. (Read Romans 1:18-2:16 and Psalm 19:1.) Thus, everyone really knows, if he is honest, that God exists and that to ignore Him has serious consequences. Further, the Bible teaches in the passage in Romans that God will judge us by the light we have received.
Even primitive societies have a concept of right and wrong, and those people know that they do not always measure up to even their own standards. One does not go to hell because he has not heard about Jesus, but because he: (a) is a sinner and falls short of God's standard, and (b) he thumbs his nose at the God he knows exists.
God's wrath is very severe toward anyone who continually rebels against Him (Nahum 1:2-6, Psalm 90:7-8). Indeed, rejecting God in any of His Trinitarian manifestations (Father, Son, or Holy Spirit) condemns one to hell. Rejecting God the Father—Romans 1:18-32. Rejecting Jesus—John 3:36; John 8:24. Rejecting the Holy Spirit—Matthew 12:31-32; Mark 3:28-29.
But the Bible also teaches that Jesus died for the sins of the whole world (1 John 2:2)! And it implies that whoever seeks after God earnestly will find him (Deuteronomy 4:29; Psalm 86:5; Proverbs 8:17; Jeremiah 29:13; Matthew 7:7-8). It also says that "If we love one another, God abides in us and his love is perfected in us." (1 John 4:12)
God is fair as well as just. We are confident, for example, that the Old Testament patriarchs, who lived by faith in God and his covenantal promises before Jesus' earthly ministry, are in heaven. So certainly some people have gotten to heaven without knowing Jesus in the personal way that the New Testament speaks of. Ultimately, only God can judge as only He knows the individual's heart. We hold out hope that, for those who have not heard but have not rejected God, for those who have been misinformed, or those who are unable to understand (children, mentally ill, etc) may be pardoned by a just God.
Certainly, the Bible does not teach "universalism." Universalism is the idea that everyone gets to heaven.
The Bible clearly teaches that the only certain way to heaven is through Jesus (John 14:6; Acts 4:12). We are confident that God will not hold anyone accountable for any knowledge he did not receive. At the same time, the Bible emphatically states that Christ is the only sure way to salvation. Anyone who has heard of the saving grace of Jesus, and rejects it, would be thumbing his nose at God (John 3:36).
To reject Jesus is a serious matter. It is tantamount to refusing God's offer of reconciliation to sinful man. As R.C. Sproul points out (book, noted in the resource list), those who have heard and reject Christ face double jeopardy. That is to say, you would be guilty by your sinful nature and guilty also for having rejected God's son. Thus "religion" without Christ does not redeem people, but may add to their ultimate guilt.
Here is a related issue: Is your religion determined by where you were born? If you are inclined to reject Christianity because of this idea, you have embraced a logical fallacy. Just as popular opinions do not determine truth, neither do circumstances or geography.