The answer to this question depends somewhat on what is meant by “living together.” If it means having sexual relations, it is definitely wrong. Premarital sex is repeatedly condemned in Scripture, along with all other forms of sexual immorality (Acts 15:20; Romans 1:29; 1 Corinthians 5:1; 6:13, 18; 7:2; 10:8; 2 Corinthians 12:21; Galatians 5:19; Ephesians 5:3; Colossians 3:5; 1 Thessalonians 4:3; Jude 7). The Bible promotes complete abstinence outside of (and before) marriage. Sex before marriage is just as wrong as adultery and other forms of sexual immorality, because they all involve having sex with someone you are not married to.
If “living together” means living in the same house, that is perhaps a different issue. Ultimately, there is nothing wrong with a man and a woman living in the same house—if there is nothing immoral taking place. However, the problem arises in that there is still the appearance of immorality (1 Thessalonians 5:22; Ephesians 5:3), and it could be a tremendous temptation for immorality. The Bible tells us to flee immorality, not expose ourselves to constant temptations to immorality (1 Corinthians 6:18). Then there is the problem of appearances. A couple who is living together is assumed to be sleeping together—that is just the nature of things. Even though living in the same house is not sinful in and of itself, the appearance of sin is there. The Bible tells us to avoid the appearance of evil (1 Thessalonians 5:22; Ephesians 5:3), to flee from immorality, and not to cause anyone to stumble or be offended. As a result, it is not honoring to God for a man and a woman to live together outside of marriage.