In Scripture there is "adultery" which is sex outside of marriage for a married person, and then there is "sexual immorality" (or in the old King James "fornication") which mainly refers to the premarital sex that the Greeks were famous for. There are other forms of sexual sin mentioned such as "homosexuality" and "prostitution".
Back when the New Testament was written, sexual immorality was much more widespread than today. Our culture is sexually degraded, to be sure, but it was much worse back in the First Century Roman empire.
For example, in the time period when the Bible was written there were church "temples" set up where sex was considered a form of worship for pagan deities. These "meetings" were essentially orgies. At night, the wail of the temple prostitutes would go out over the city, and men and boys would respond like lemmings since this was the way they were raised. They thought this was "religion"!
Imagine, in that licentious and perverted culture, how the strict teachings of the New Testament (that no sexuality is permitted by God outside of marriage) must have gone over. "You have got to be kidding, I can never go to the shrine prostitutes again? What if I like somebody? What if I want or need to have sex? You mean to tell me that to be a Christian that I can't have any sex at all outside of marriage? That is a bit much, really!"
The point is that our culture now--bad as it is--is not as sexually promiscuous as the culture that the New Testament was written in, and God says a clear "no" to fornication/sexual-immorality in no uncertain terms, and with the sternest of warnings and consequences.
The notion that the scriptures forbidding sexual promiscuity no long apply to us because of modern "sexual liberation" is completely without merit. The teachings of Christianity were as radical back then as they are now, only more so back then. If Christ in them can live by such standards, then Christ in us can as well.
Here are a few texts...
1Thes 4:2-5 (NIV) For you know what instructions we gave you by the authority of the Lord Jesus. It is God's will that you should be sanctified: that you should avoid sexual immorality; that each of you should learn to control his own body in a way that is holy and honorable, not in passionate lust like the heathen, who do not know God.
Gal 5:19 (NIV) The acts of the sinful nature are obvious: sexual immorality, impurity and debauchery.
Eph 5:3 (NIV) But among you there must not be even a hint of sexual immorality, or of any kind of impurity, or of greed, because these are improper for God's holy people.
Heb 12:16 (NIV) See that no-one is sexually immoral, or is godless like Esau, who for a single meal sold his inheritance rights as the oldest son.
Re 21:8 (NIV) "But the cowardly, the unbelieving, the vile, the murderers, the sexually immoral, those who practice magic arts, the idolaters and all liars--their place will be in the fiery lake of burning sulphur. This is the second death."
1Cor 5:9-11 (NIV) I have written to you in my letter not to associate with sexually immoral people--not at all meaning the people of this world who are immoral, or the greedy and swindlers, or idolaters. In that case you would have to leave this world. But now I am writing to you that you must not associate with anyone who calls himself a brother but is sexually immoral or greedy, an idolater or a slanderer, a drunkard or a swindler. With such a man do not even eat.