I assume by your question you are referring to living with someone outside of the marriage bond. Living with someone of the opposite sex exposes both parties to sexual temptation and relationships which are strictly forbidden in Scripture (see Gen. 2:23-24; Eph. 5:22-33; 1 Thess. 4:1-12). We sometimes hear of situations where a man and a woman may share an apartment in a strictly business-like relationship (just sharing the rent and space as roommates, nothing more), but this opens each of them up to unnecessary risks and temptations. In other words, it is playing with fire.
The Bible teaches us to flee from temptation. One of the simple reasons is that God designed sex to be a part of a relationship of commitment where two people devote themselves to each other as partners for life (again cf. Gen. 2:23-24). They are to be devoted to, complement, and fulfill one another in a loving and sacrificial relationship where each partner seeks to minister to the other person. Co-habitation situations will nearly always lack this commitment.
While sex is designed for both procreation and joyous intimacy and pleasure, it was nevertheless to be a part of one’s commitment to the other person in marriage. Without this, what you have is simply the exploitation of the other person for selfish purposes, and more often than not, it is the woman who gets exploited. Without the commitment of marriage, there will rarely be the willingness needed to work through the problems that will be encountered. When a relationship doesn’t work out and children are involved, the woman is generally left to raise the children as a single parent, which is contrary to God’s plan for the family unit.
There is a study on 1 Thessalonians 4:1-12 on our web site which deals with the proper approach to marriage.
All of this goes contrary to today’s ideas, but as the Bible teaches us, “There is a way that seems right to man, but the end is the way of death” (see Prov. 14:12 along with 12:15; 16:2; 21:2).
I’m sure there are other sites that deal with this issue. Take a look at Probe at http://www.probe.org. This is an excellent site that deals with current social issues. They may be able to help and have someone who has addressed this issue.