For follow-up discussion and general commentary on the topic. Comments are sorted chronologically.
"But I say to the unmarried and to the widows: g It is good for them if they remain even as I am; 9 but h if they cannot exercise self-control, let them marry. For it is better to marry than to burn with passion."
I Corinthians 7:8
It is important to keep in mind the historical/cultural and linguistic contexts when examining Jesus' statements in Matthew 5, Mark 10, and Luke 16 concerning divorce and remarriage. Contrary to popular belief, diligent examination of the Greek syntax used reveals that Jesus did not permit divorce for marital infidelity. He states that anyone who "divorces" (APALUO) his wife except for "fornication/sexual immorality" (PORNEIA) causes her to commit "adultery" (MOICHAO).
Remember that these people that Jesus is talking to are 1st century Jews living under Torah law. The Torah mandates that adultery is a capital crime (Lev 20:10), so what we understand divorce to be would be a moot point. The offending party would be executed, provided that there were at least 2 witnesses (Deut 17:6). Jesus would hardly set himself up to be "least in the kingdom," per his own words in Matt 5:19. Again, keep in mind that his audience in these passages are groups of Jews. They would have railed him for speaking contrary to the scriptures. Furthermore, if he had spoken contrary to the Law, he would be contradicting himself, as well as disqualifying himself from being the true Messiah.
The fact that he uses a completely different word for fornication (PORNEIA) than he uses for adultery (MOICHAO) should alert us to different meanings. The word MOICHAO is straightforward, meaning exactly what we understand it to mean - adultery. However, the word PORNEIA is used as an umbrella term indicating any illegal sexual union, i.e. incest, homosexuality, beastiality, marriage to someone worshiping another god, and, interestingly, according to Jesus' use of the word, marriage to someone divorced. In other words, he is stating that he only permits divorce if the relationship ITSELF is a forbidden relationship to begin with, which would essentially be repenting from becoming involved with someone that one shouldn't have gotten involved with in the first place, according to what God had stated in his word. An OT example of this occurring is in Ezra 10, where they had taken foreign wives who refused to forsake pagan worship (see Exodus 34:15-16). Had the wives forsaken pagan idolatrous worship like Rahab and Ruth did, the Israelites would have been perfectly welcome, as far as God was concerned, to marry them.
I know this is a bitter horse pill to try and swallow for a lot of people, and I can sympathize, but this is the teaching of Jesus in the original Greek, and even though gentile believers are not beholden to Mosaic/Torah law, this term (PORNEIA) is included in the apostolic decree in Acts 15.
Paul echoes this teaching, using the same word, in his letters, with the exception of someone being abandoned for converting to the faith, who is then allowed to remarry, "only in the Lord."
All of these answers are correct, but there is another element that has not been touched on. As believers don't the elders, as in Biblical times, need to instruct the engaged couple?
Something that is missing in modern Christian settings is the imparting of wisdom from one generation to the other. Today families are isolated from one another. There seems to be little if any instruction that the body of believers is involved in.
The wisdom of grandparents is discarded, as is the aunts and uncles, or even the neighbor. In today's world rarely do we receive instruction before the event. We seem to always be dealing with the wreckage or the aftermath.
There are too many areas in today's body of believers where we abdicate the responsibility of teaching what God would have us do. It doesn't matter that you've known each other since the third grade. What if God's choice for your spouse doesn't come along until you are an adult? The sad thing is when you realize this you are already in a marriage that God never intended.
Everyone who has commented here knows someone who is locked in a marriage that is not productive, that does not serve the Lord as a couple because they are so miserable in the mistake they made by not seeking the Lord's guidance in the first place.
Don't we as believers share the responsibility of helping two people understand the seriousness of marriage and the will of God? Young men today don't sit on the steps of the temple or the church and learn from the elders how to treat women, especially their wives. Young women don't sit at the feet of wise women and learn how she should treat her husband or how she should expect to be treated by her husband.
More time is spent on picking out the dress, ordering invitations and the cakes and making sure the church is available and making sure the groom knows that he is supposed to give thank you gifts to his groomsmen and ushers, and so on and so on.
How much time is ever spent on helping the couple find out if they are really meant for each other, or if it is God's desire that they should be married? You just shouldn't have to make a commitment as important as marriage without some help in the matter. I have no scriptures to offer, but I do know that you know what I am talking about.