Is there a sin that God will not pardon?

According to the teachings of Jesus there is a sin that is not forgivable. In Matthew 12, a demon possessed man is brought to Jesus, who in turn casts the demon from the man. The Jewish leaders in the form of the Pharisees accuse Jesus in being in league with Satan. Jesus then states that satanic forces do not work against satanic forces, but that instead the work He is doing is that of the Holy Spirit. In Matthew 12:31-32(NIV), Jesus says:
Therefore I say to you, every sin and blasphemy will be forgiven men, but the blasphemy against the Spirit will not be forgiven men. Anyone who speaks a word against the Son of Man, it will be forgiven him; but whoever speaks against the Holy Spirit, it will not be forgiven him, either in this age or in the age to come.

Jesus here is stating that to attribute the work of the Spirit to the work of Satan is to blaspheme the Holy Spirit.

Okay, important safety tip... Thanks, Egon. Ummm... wait, what exactly is "blasphemy against the Holy Spirit?"

To understand this sin, one must understand the role that the Holy Spirit plays in the process of salvation. Prior to salvation, the Holy Spirit's role is one of revelation and conviction.

First, the Holy Spirit reveals the truth to non-believers. 1 Corinthians 2:14(NIV) states:

The man without the Spirit does not accept the things that come from the Spirit of God, for they are foolishness to him, and he cannot understand them, because they are spiritually discerned.

This means that even the truth of the Gospel is not discernable to an unregenerate man because he does not have at that point within him the ability to see it as such. It is, therefore, the role of the Holy Spirit to reveal to those who do not believe the truth of the life of Jesus and His identity as Messiah and in doing so, convince the person of their need to identify their life with the atoning work of Jesus on the cross and in doing so make Him their Lord.

A person who has this occur in their life and refuse to believe or act upon the conviction brought into their life by the Holy Spirit is guilty of what Jesus refers to as blasphemy of the Holy Spirit. If the person reaches the end of their days of life on this earth and has not believed in Christ, there is no forgiveness for them - they have chosen not to believe on Christ and according to Scripture have chosen instead to live for eternity away from the presence of God and Christ. What Jesus is teaching is that should you reach the end of your life without having made a decision in this life to follow Him, you have no opportunity to repent of that decision beyond the grave, because there is no forgiveness for denying the leading of the Spirit.

Okay, that seems to make some sense. But I have always heard that suicide was an unpardonable sin, because by taking your life you won't have an opportunity to ask forgiveness and be pardoned. What about that?

This is a well-known teaching from some faiths. It is often brought up in conversation, especially when someone has died by their own hand. Unfortunately, it does not seem to have a scriptural basis.

The thing about this teaching is that it hinges on the fact that a person cannot ask for forgiveness before they die. But if that were the case, then if I as a Christian were to say a harsh word to someone, lie, steal, cheat, lust after a woman or any of a number of other sins, and then get struck by a car and die before I have an opportunity to ask for forgiveness, logic would dictate that I too would be destined for Hell. This however is not a teaching that you hear, though it would seem to be a much more likely scenario.

The upshot is that while the Scriptures discuss the premature ending of a person's life by their own hand, it never states that the person will be damned for the act. Suicide is horrible and sad and from a spiritual viewpoint, it is a sin. It effectively is telling God that you don't trust Him to do with your life what is best by following His plan and believing that He will do what is best and instead deciding that you know what is right. This is effectively what we all do everytime we sin, it is just that suicide has more long lasting consequences, but it is not a sin that is "unpardonable" and will sentence a person to Hell if they are already a Christian.