Without any marital agreement, contract, or civil action... it is generally considered to be fornication. However, as Godsdrummer stated, it's not the unforgiveable sin. Paul wrote an admonition for couples who cannot control their passion for one another...
I Corinthians 7:8-9 (ESV)
8 To the unmarried and the widows I say that it is good for them to remain single as I am. 9 But if they cannot exercise self-control, they should marry. For it is better to marry than to burn with passion.
So, if a couple (or a single individual) cannot restrain their passions, they should consider marriage.
Some ministers I know have applied premarital relations to this text...
I Corinthians 7:36 (ESV)
36 If anyone thinks that he is not behaving properly toward his betrothed, if his passions are strong, and it has to be, let him do as he wishes: let them marry—it is no sin.
It appears that there is disagreement between various ministers as to what the phrase "not behaving properly" means. Most say that it means that if a man doesn't feel that he's behaving properly by putting off the wedding, they should just go ahead and get married. Others argue that the reference to "passions" indicates a sexual impropriety. Thus, they would argue that this means that if a betrothed couple cannot restrain their passions, they should do as the wish (stay the course of the relationship), but marry. Here are some additional translations of this verse for further consideration:
1 Corinthians 7:36 (NLT)
36 But if a man thinks that he’s treating his fiancée improperly and will inevitably give in to his passion, let him marry her as he wishes. It is not a sin.
1 Corinthians 7:36 (NIV)
36 If anyone is worried that he might not be acting honorably toward the virgin he is engaged to, and if his passions are too strong[a] and he feels he ought to marry, he should do as he wants. He is not sinning. They should get married.
1 Corinthians 7:36 (NKJV)
36 But if any man thinks he is behaving improperly toward his virgin, if she is past the flower of youth, and thus it must be, let him do what he wishes. He does not sin; let them marry.
1 Corinthians 7:36 (CEB)
36 If someone thinks he is acting inappropriately toward an unmarried woman whom he knows, and if he has strong feelings and it seems like the right thing to do, he should do what he wants—he’s not sinning—they should get married.
1 Corinthians 7:36 (AMP)
36 But if any man thinks that he is not acting properly toward and in regard to his virgin [that he is preparing disgrace for her or incurring reproach], in case she is passing the bloom of her youth and if there is need for it, let him do what to him seems right; he does not sin; let them marry.
1 Corinthians 7:36 (CEV)
36 But suppose you are engaged to someone old enough to be married, and you want her so much that all you can think about is getting married. Then go ahead and marry. There is nothing wrong with that.
1 Corinthians 7:36 (HCSB)
36 But if any man thinks he is acting improperly toward his virgin,[a] if she is past marriageable age,[b] and so it must be, he can do what he wants. He is not sinning; they can get married.
Kehillah in I Corinthians 7:36 Orthodox Jewish Bible (OJB)
36 However, if anyone thnks he does not have proper hitnahagut (conduct) toward the betulah of his eirusin (betrothal, engagement), and if he thinks his basherte (destined mate) is getting along in years, and thus it has to be, what he desires, let him do; there is no chet, let them enter bibrit hanissuim (in convenant of marriage).
1 Corinthians 7:36 The Voice (VOICE)
36 But I have this advice for every single man: If anyone thinks he is behaving badly toward his fiancée, if his desires prove to be too much for him, and if he feels they ought to marry, then he should do what he wants; it is not wrong to marry her. It is better that we let men and women in this situation do as they wish and get married.
In the Law of Moses we read...
Deuteronomy 22:28-29 (ESV)
28 “If a man meets a virgin who is not betrothed, and seizes her and lies with her, and they are found, 29 then the man who lay with her shall give to the father of the young woman fifty shekels of silver, and she shall be his wife, because he has violated her. He may not divorce her all his days.
So, this would mean that if a man seduces an un-betrothed or un-married woman, and the act is discovered, then the man who seduced her is to give her father fifty shekels of silver, and she is assigned as his wife. He is forbidden to divorce her and must keep her as a wife for life.
Marital customs differ from country to country, culture to culture, and even from Christian community to Christian community. Early Christians recognized self-officiated unions, even if the couple gave their vows to one another alone behind a barn. These became known as "illicit marriages" in the early stages of the rise of the Catholic church, after the requirement for a priest or bishop to be present as a witness was established. Some churches will bless a couple's union as being one of "holy matrimony" even if they have yet to make it legal through civil process. Some Christian communities (such as the Quakers" will marry a couple in their gathering/meeting and leave the decision to make it "legal" through the civil process entirely up to the couple.
There appears to be no clear cut definition, description, or ceremony for marriage detailed in Scripture beyond a private agreement and/or private contract between the couple and/or their families. The church traditionally has reserved the right to either bless or condemn any given relationship. For example, some Catholic and Church of God in Christ churches will not bless civil marriages wherein one or both members of the union were previously married. Many churches will only bless a second civil marriage if the previously married individual(s) divorced on the grounds of adultery. Quakers and more libertarian Christian churches will bless unions privately as being marriages in "God's eyes" although the couple has yet to get or doesn't desire a civil marriage.
Several Reformed Baptist congregations that I know openly accept unmarried couples who live together prior to marriage. Their position is that living together prior to marriage is the "custom" of our culture. Therefore, it isn't a "sin" as it was in New Testament times wherein the culture overall condemned living together before marriage. They argue that without a clear cut biblical edict on marital custom, culture and legality define the terms as it might relate to faithfulness, sexual immorality, engagement (betrothal), and marriage.
Perhaps the best position to take is that it is up to each individual body to manage unmarried couples and their prospective marriages as they feel led of the Spirit.