The clearest statement of this is in 1 Corinthians 7

8 Now to the unmarried and the widows I say: It is good for them to stay unmarried, as I am.

9 But if they cannot control themselves, they should marry, for it is better to marry than to burn with passion.

This clearly shows that for Paul there are only two options - have sex within marriage or not at all - at least with another person.
See:
http://www.biblegateway.com/passage/?book_id=53&chapter=7&version=64

The whole passage is interesting in this context: the previous chapter has the words:

18 Flee from sexual immorality. All other sins a man commits are outside his body, but he who sins sexually sins against his own body.

[ i.e sexual sin is especially damaging compared with others]
Continuing:

19 Do you not know that your body is a temple of the Holy Spirit, who is in you, whom you have received from God? You are not your own;

20 you were bought at a price. Therefore honour God with your body.

This is remarkably strong language - yet preachers today try to downplay the importance of sexual sin. In fact Paul talks about it a lot, reflecting the fact that it was a major feature of the culture in which he was planting churches, and an area where the standards of the culture were substantially different from those of the church. By contrast Jesus doesn't say much about it because the culture of his listeners had no doubt about sex outside marriage being wrong.

This is not popular in modern society, but if we are to be faithful to the gospel that our God would have us proclaim, it is a line we should be holding clearly and unambiguously