Salvation

Evangelists are Christians engaged in the task of persuading others to repent and believe the gospel, the Christian way of salvation. (See this page for a presentation of the gospel.) People who have never heard the gospel are called unevangelized. People who are not currently involved in a church that teaches the gospel are called unchurched, whether they themselves have heard the gospel or not.
Evangelical Christians have traditionally held that belief in the gospel is the only way to receive forgiveness from God and spend eternity in heaven. This view is called exclusivism. Some teachers hold to inclusivism, the belief that while Christianity is the only true religion, some God-fearing people may come to salvation without having heard or accepted the gospel. Still more radical is religious pluralism, the belief that God genuinely brings people to salvation through many religions, not just Christianity. The most inclusive view is universalism, the belief that everyone will ultimately receive salvation from God and spend eternity in heaven.
The Bible teaches that Christians are chosen from eternity by God, but that people must choose to embrace the gospel in order to be saved. The earlist Protestant explanation of how these teachings go together is Calvinism. Calvinism stresses the freedom and determining power of God. Full (5-point) Calvinists believe that all people are morally unable to accept God until regenerated by the Holy Spirit, that God chooses individuals for salvation unconditionally, that Christ's death paid the penalty for the sins of only those elect, and that the Spirit's work makes their salvation certain, both before and after they embrace the gospel. However, God uses human means to achieve His purposes, so that sinners are converted through the preaching of the gospel. See this article for an in-depth look at Calvinism. The theological system based on Calvinism is often called Reformed theology, which also places a heavy emphasis on biblical inerrancy and substitutionary atonement. (Reformed is also the name of a family of denominations, and can be used to designate specifically Presbyterian theology. I use it more broadly to identify the common doctrine of the Magisterial Reformers Luther, Calvin, Zwingli, Knox, and the Puritans and Particular Baptists.)
Some theologians have departed from Calvinism for hyper-Calvinism (which they prefer to call "high Calvinism"). This view denies the need for evangelism, missions, and repentance, and instead emphasizes the need for introspection to learn whether a person is among the elect. Hyper-Calvinism also claims that God has no love or compassion for those who are not elect.
A more popular alternative to Calvinism is Arminianism, which stresses the free and self-determining will of man. Full Arminians believe that all people are morally able to accept God, that God chooses people for salvation based on His knowledge of who will one day believe, that Christ's death made atonement possible for everyone, and that people always retain the ability to reject God's salvation, both before and after they embrace the gospel. Most Baptists who are generally Arminian nevertheless believe in eternal security, the belief that it is impossible for a truly saved person to lose that salvation.
One way in which Calvinists and Arminians tend to differ is in their view of revival. Revival is marked by greater spiritual fervor among Christians, often accompanied by a greater-than-usual number of conversions among sinners. Calvinists see revival as a surprising, sovereign work of the Holy Spirit that believers can pray for but cannot manufacture. The Arminian approach, often called revivalism, seeks to bring about revival through human methods, and attributes the presence or absence of revival to humans' willingness to cooperate with what the Spirit wants to accomplish.
How is a person justified, declared righteous before God? The Catholic church teaches sacramentalism, in which saving grace for the forgiveness of sins comes through the proper exercise of sacraments such as baptism, the Mass (the Lord's supper), and confession. Many Protestants believe a form of this called baptismal regeneration, in which the blessings of salvation are conferred when a person is baptized. The primary evangelical view is justification by faith, in which a person who has faith in Christ alone for salvation has His sins forgiven as a result of Christ's work on the cross. Related is imputed righteousness: Christ's obedience is reckoned to or bestowed on the convert, given as an act of God's grace apart from works and received by faith alone. However, some recent scholars have developed a new perspective on justification in which a person's own good works play a significant part in determining his ultimate salvation.
One other debate about salvation is whether saving faith must involve repentance, or else consists simply in trusting in Jesus' sacrifice for the forgiveness of sins. Lordship salvation is the traditional view and holds that saving faith must involve a commitment to repent of one's sins and follow Christ as Lord. Those who also believe that salvation cannot be lost would then argue that Christians who do not persevere in obedience to Christ did not have genuine faith. The alternative view is that salvation is promised to all who rely on the saving work of Christ for forgiveness, and that a lack of repentance results only in the loss of rewards. Often this results in a two-tiered view of salvation, in which there are true Christians who have never repented but have Jesus as their Savior, and those who do repent break through to a higher level of Christian life in which Jesus is also their Lord.