Can Remarry?
Those NEVER MARRIED and WIDOWS can remarry if they want to. 

1 Cor 7:8  But I say to the unmarried and to widows that it is good for them if they remain even as I.  9  But if they do not have self-control, let them marry; for it is better to marry than to burn... 39  A wife is bound as long as her husband lives; but if her husband is dead, she is free to be married to whom she wishes, only in the Lord.  40  But in my opinion she is happier if she remains as she is; and I think that I also have the Spirit of God.

WIDOWS are encouraged NOT to remarry if they are over 60. They are supported by the church when they don't have family to support them.

1 Tim 5:3  Honor widows who are widows indeed... 5  Now she who is a widow indeed, and who has been left alone has fixed her hope on God, and continues in entreaties and prayers night and day... 9  Let a widow be put on the list only if she is not less than  sixty   years  old, [having been] the wife of one man,  10  having a reputation for good works; [and] if she has brought up children, if she has shown hospitality to strangers, if she has washed the saints' feet, if she has assisted those in distress, [and] if she has devoted herself to every good work... 16  If any woman who is a believer has [dependent] widows, let her assist them, and let not the church be burdened, so that it may assist those who are widows indeed. 


1 Tim 5:11  But refuse [to put] younger widows [on the list], for when they feel sensual desires in disregard of Christ, they want to get married, 12  [thus] incurring condemnation, because they have set aside their previous pledge... 14  Therefore, I want younger [widows] to get married, bear children, keep house, [and] give the enemy no occasion for reproach.

What about those who are DIVORCED?
One whose unbelieving spouse leaves (divorces) THEM may remarry. In such cases, they are no longer under bondage, or bound to a spouse.  However, a believer is NOT to seek a divorce from an unbeliever.

1 Cor 7:12  But to the rest I say, not the Lord, that if any brother has a wife who is an unbeliever, and she consents to live with him, let him not send her away.  13  And a woman who has an unbelieving husband, and he consents to live with her, let her not send her husband away.  14  For the unbelieving husband is sanctified through his wife, and the unbelieving wife is sanctified through her believing husband; for otherwise your children are unclean, but now they are holy.  15  Yet if the unbelieving one leaves, let him leave; the brother or the sister is not under bondage in such [cases,] but God has called us to peace.

And by implication...
One who divorces because of porneia MAY remarry, because the scripture expressly states that one who divorces for any other cause CANNOT remarry without committing adultery.

Matt 19:3  And [some] Pharisees came to Him, testing Him, and saying, "Is it lawful [for a man] to  divorce  his wife for any cause at all?"  4  And He answered and said, "Have you not read, that He who created [them] from the beginning made them male and female,  5  and said, 'For this cause a man shall leave his father and mother, and shall cleave to his wife; and the two shall become one flesh'?  6  "Consequently they are no longer two, but one flesh. What therefore God has joined together, let no man separate."  7  They said to Him, "Why then did Moses command to give her a certificate of  divorce  and send [her] away?"  8  He said to them, "Because of your hardness of heart, Moses permitted you to  divorce  your wives; but from the beginning it has not been this way.  9  "And I say to you, whoever  divorces  his wife, except for immorality, and marries another woman commits adultery. 10 "The disciples said to Him, "If the relationship of the man with his wife is like this, it is better not to  marry." 

One who separates/divorces from his/her spouse when there has been no immorality CANNOT remarry.  They are encouraged to remain single or else to be reconciled.

1 Cor 7:10  But to the married I give instructions, not I, but the Lord, that the wife should not leave her husband  11  (but if she does leave, let her remain unmarried, or else be  reconciled  to her husband), and that the husband should not send his wife away.

Who else CANNOT remarry?
One who is still married cannot remarry.

Rom 7:2  For the  married  woman is bound by law to her husband while he is living; but if her husband dies, she is released from the law concerning the husband.  3  So then if, while her husband is living, she is joined to another man, she shall be called an adulteress; but if her husband dies, she is free from the law, so that she is not an adulteress, though she is joined to another man. 

One CANNOT remarry a FORMER SPOUSE after they have married  another.

Deut 24:1  "When a man takes a wife and marries her, and it happens that she finds no favor in his eyes because he has found some indecency in her, and he writes her a certificate of  divorce  and puts [it] in her hand and sends her out from his house,  2  and she leaves his house and goes and becomes another man's [wife,]  3  and if the latter husband turns against her and writes her a certificate of  divorce  and puts [it] in her hand and sends her out of his house, or if the latter husband dies who took her to be his wife,  4  [then] her former husband who sent her away is not allowed to take her again to be his wife, since she has been defiled; for that is an abomination before the Lord, and you shall not bring sin on the land which the Lord your God gives you as an inheritance.

 Stay the way you are (single, if possible)!

1 Cor 7:24  Brethren, let each man remain with God in that [condition] in which he was called... 26  I think then that this is good in view of the present distress, that it is good for a man to remain as he is.  27  Are you bound to a wife? Do not seek to be released. Are you released from a wife? Do not seek a wife.  28  But if you  should   marry , you have not sinned; and if a virgin  should   marry , she has not sinned. Yet such will have trouble in this life, and I am trying to spare you. 29  But this I say, brethren, the time has been shortened, so that from now on those who have wives  should  be as though they had none;  30  and those who weep, as though they did not weep; and those who rejoice, as though they did not rejoice; and those who buy, as though they did not possess;  31  and those who use the world, as though they did not make full use of it; for the form of this world is passing away.  32  But I want you to be free from concern. One who is unmarried is concerned about the things of the Lord, how he may please the Lord;  33  but one who is married is concerned about the things of the world, how he may please his wife,  34  and [his interests] are divided. And the woman who is unmarried, and the virgin, is concerned about the things of the Lord, that she may be holy both in body and spirit; but one who is married is concerned about the things of the world, how she may please her husband.  35  And this I say for your own benefit; not to put a restraint upon you, but to promote what is seemly, and [to secure] undistracted devotion to the Lord.

Marriage According to the World; 
Adultery According to the Lord
Biblical Grounds for Divorce

Questions? Comments?

4202. porneia, aV porneia; from 4203 ; fornication :-- fornication(4), fornications(2),
immoralities(1), immorality(16), sexual immorality(m)(1), unchastity(1)