This has been a most interesting thread to watch.
There is a great deal within this thread on which to make comment. I will comment to the opening poster's question.
From what I have learned in the Bible, I see no marriage after divorce while the spouse is living. As is spoken by Jesus in Matt 19:8 He saith unto them, Moses because of the hardness of your hearts suffered you to put away your wives: but from the beginning it was not so.
God is not the author of divorce. It is not what He wants. The evil desires of man are the cause of divorce. Jesus tells us in this passage that Moses did this because of their hard hearts, I see Him giving no credit to God for this action for it is not his will. As with many things we've read about in the Old Testament, God permitted Isreal to be lost in overwhelming sin on many occasions. They are some of our most expounding examples of what not to do when it comes to the word of God.
All marriage is sacred, as are all vows into God's covenant of marriage, which are wittnessed by God (Malachi 2:14 "Yet ye say, Wherefore? Because the Lord hath been witness between thee and the wife of thy youth, against whom thou has dealt treacherously: yet is she thy companion, and the wife of thy covenant."
Marriage is God's created covenant, and He acknowledges the union of each and every marriage being done, whether they are right or wrong. All will be judged according to the Word.
Yes, there is scripture giving one reason to put away in divorce and even to let a spouse leave and not have to go with them, but the Bible is silent in the New Testament regarding remarriage except in the case of death, and even that has restrictions.
1 Cor 7:39
39 The wife is bound by the law as long as her husband liveth; but if her husband be dead, she is at liberty to be married to whom she will; only in the Lord.
What law? James 5:12
12 But above all things, my brethren, swear not, neither by heaven, neither by the earth, neither by any other oath : but let your yea be yea; and your nay, nay; lest ye fall into condemnation.
I believe "I do" is a "yea".
Physical contact is to be between a husband and wife only and their union is life long by their vows, no matter how people try to chop it up.
1 Cor 7:1-2
7:1 Now concerning the things whereof ye wrote unto me: It is good for a man not to touch a woman .
2 Nevertheless, to avoid fornication, let every man have his own wife, and let every woman have her own husband.
And it is to remain between them, no others ever, until death they do part. It is sin to even look at someone with lust. Matt 5:27-28
27 Ye have heard that it was said by them of old time, Thou shalt not commit adultery:
28 But I say unto you, That whosoever looketh on a woman to lust after her hath committed adultery with her already in his heart .
Single man? Married man? It doesn't matter, it's wrong to do.
There are some "clincher" verses that spell much out specifically on this subject. They are direct statements. As with many things within the Bible, put them all together to get the full picture. If it says "don't do this" in one verse, don't do it. If it says "you are that if you do this" then consider yourself that if you decide to do this. Here are some of the "clincher" verses:
I noticed Matthew 19:9 posted earlier. That is a twin statement to this next verse, though this next verse expounds more fully the meaning of that which is echoed in Matthew 19:9, since this next verse came earlier:
Matt 5:32
32 But I say unto you, That whosoever shall put away his wife, saving for the cause of fornication, causeth her to commit adultery: and whosoever shall marry her that is divorced committeth adultery.
In other words, if the divorce writer should leave his unsinful wife and she would again marry, she would be guilty of adultery, but he would be guilty of causing her to commit adultery.
Another "clincher" verse set would be this (I can just imagine Jesus looking at the diciples, having to repeat himself on the subject and being very point blank about His additional response):
Mark 10:2-12
2 And the Pharisees came to him, and asked him, Is it lawful for a man to put away his wife? tempting him.
3 And he answered and said unto them, What did Moses command you?
4 And they said, Moses suffered to write a bill of divorcement, and to put her away.
5 And Jesus answered and said unto them, For the hardness of your heart he wrote you this precept.
6 But from the beginning of the creation God made them male and female.
7 For this cause shall a man leave his father and mother, and cleave to his wife;
8 And they twain shall be one flesh: so then they are no more twain, but one flesh.
9 What therefore God hath joined together, let not man put asunder.
(Now, that should be enough right there but they just wouldn't let the subject drop)
10 And in the house his disciples asked him again of the same matter.
11 And he saith unto them, Whosoever shall put away his wife, and marry another, committeth adultery against her.
12 And if a woman shall put away her husband, and be married to another, she committeth adultery.
Here are other verses that some tend to use as a reason to remarry though these scriptures, themselves, speak nothing of remarriage at all:
1 Cor 7:12-16
12 But to the rest speak I, not the Lord: If any brother hath a wife that believeth not, and she be pleased to dwell with him, let him not put her away.
13 And the woman which hath an husband that believeth not, and if he be pleased to dwell with her, let her not leave him.
14 For the unbelieving husband is sanctified by the wife, and the unbelieving wife is sanctified by the husband: else were your children unclean; but now are they holy.
15 But if the unbelieving depart, let him depart. A brother or a sister is not under bondage in such cases: but God hath called us to peace.
16 For what knowest thou, O wife, whether thou shalt save thy husband? or how knowest thou, O man, whether thou shalt save thy wife?
Ok, so now we have:
1. If you put your wife away and marry another, you commit adultery.
2. If you put your husband away and marry another, you commit adultery
3. If you marry a divorced woman, you commit adultery.
4. If you put away a wife that has not fornicated, you cause her to commit adultery and you are at fault.
5. You can put a wife away that fornicated because she has committed adultery.
6. If the unbelieving spouse really wishes to leave the union, let them go
7. A woman can marry again if her husband is dead, and then, only to a Christian.
In 1-6 I have read no permission to remarry by God. Why? Because the spouse is still alive.
From what I have seen thus far, the scriptures of the New Testament are silent regarding remarriage except in death. Does that mean we fill in the blanks?
I mean no offense to anyone. Please study the scriptures for yourself.
Remember, 1 Cor 14:33 God is not the author of confusion.
His preference is all we should do.
(I'm very sorry this ended up so long. It wasn't supposed to do that)