Luke 13:3 "I tell you nay, but except ye repent, ye shall all likewise perish." (also repeated in v.5)
Repentance simply means a turning from sin and self unto Christ. Unless a person is willing to turn from their sin and self there can be no Salvation. It is unfortunate that even in our own circle (Independent Fundamental Baptists) that repentance is the subject of some intense debate. I personally believe that repentance has been redefined to mean penance. If that be the case, then I would affirm that repentance is not necessary to Salvation. However, the Bible tells us what repentance is and what it does. Furthermore, it tells us very plainly in the text above, that without genuine repentance, sinners will perish. Jesus Christ himself, says that He calls sinners to repentance in Luke 5:32. Repentance is a necessary aspect of evangelism, so much so that repentance and remission of sins are matters to be declared among "all nations" in Luke 24:7.
2 Cor. 7:10 says: "For godly sorrow worketh repentance to salvation not to be repented of: but the sorrow of the world worketh death." A person must understand sin, and their sinfulness. In other words, they must first "get lost" before they can "get saved." They must agree with God concerning their sin, and the just penalty of their sin. Unless they see their sin, they will not see the need for a Savior. This I believe, is the reason why people do not want to get saved. They love their sin so much that they are not even willing to agree with God against it.
Diminish repentance and a Catholic will affirm that Christ is both Savior and Lord, and yet cling to their sacramentalism. A polytheist would simply "add" Christ among his many gods. A Christian cannot and must not by-pass this important doctrine.
Repentance is not restricted to the conversion of the unsaved. It is also a significant doctrine relevant to every believer. Repentance and restitution are tools whereby a brother or sister in Christ can be restored to spiritual maturity and usefulness for Christ and the ministry. In Luke 17:3, Jesus said: "Take heed to yourselves: If thy brother trespass against thee, rebuke him; and if he repent, forgive him." We as Christians, have a responsibility to rebuke and forgive. A brother is to be rebuked for trespassing, but and if or when a brother "repents," then, they must be forgiven. You can know that a brother is repentant when they don't live down their faults, or sins.