What is the basis for the idea that marriage requires a ceremony?

Who says there wasn't a ceremony? The very definition of marriage is the legally or formally recognized ritual of union between a man and a woman, and the definition of ceremony is an event of ritual significance. God created Eve and gave her to Adam so that they could populate the whole Earth, sounds like a pretty significant event to me.

In some cultures, simply 'doing it' was in itself an act of commitment and considered a marriage. We don't live in one of those cultures.

The fact that this question is being asked–in my mind–seems to allude to a fulfilling of this scripture:

"Now the Spirit speaketh expressly, that in the latter times some shall depart from the faith, giving heed to seducing spirits, and doctrines of devils; Speaking lies in hypocrisy; having their conscience seared with a hot iron; Forbidding to marry, and commanding to abstain from meats, which God hath created to be received with thanksgiving of them which believe and know the truth." (1 Tim 4:1-3)

In these latter times, there certainly seems to be an increasingly popular rational for couples to live or be together without getting married. Asking for the Biblical basis for a marriage ceremony to me seems like it would precede a cunning argument against having a marriage ceremony.

Where's the Biblical Basis?

"Thou shalt not commit adultery:" (Ex. 20:14;)

What is adultery in the context of this scripture?

Adultery is the unlawful association of men and women.

The law in most nations requires a ceremony for a marriage to be recognized. In ancient times there were a lot of laws about marriage which involved betrothals and contracts and proof of virginity, etc, etc...

God married Adam and Eve when he created Eve and gave her to Adam. I imagine after that, the first ceremony not performed by a deity would have been when Adam gave away his first daughter as a wife. I don't know if anyone has ever questioned the necessity of having a marriage ceremony up until these latter times that Paul alluded to.

Someone once remarked on a different SE website, "Etymology is not my destiny," or something to that effect. To that person, where a word came from and the meaning of that word when it came into existence should not control its meaning for him today, whether today is 10 years ago or 10,000 years ago. I would add to that sentiment by suggesting that meanings aren't so much in words as they are in people. Moreover, the meanings and connotations of words evolve, come into and go out of fashion, and even disappear altogether, only to re-emerge later with the same, different, or more or less nuanced meanings.

That said, the word ceremony, which you used in your question, was derived from the "Medieval Latin cēremōnia, from Latin caerimōnia, what is sacred, a religious rite.". Today, however, the meaning of ceremony brings to mind such things as formality, protocol, "dressing up," "by invitation only," and an official setting, whether it's on a beach or in a cathedral. A ceremony today is an occasion that is seldom an ad hoc thing but is planned for, organized, and has an expected protocol and significance attached to it. Put differently, there is still something special about a ceremony today, even though the religious and sacred denotations of the word have largely faded into the background in the minds of many people.

According to a study published by TheKnot.com and WeddingChannel.com in March 2013, one trend in weddings in America could be described as "less religion and more informality":

"[The] number of weddings taking place in religious institutions [is] declining. In hand with the move toward more-casual weddings, religious institutions are chosen less frequently for the wedding ceremony. Only 35% of brides opted to hold their wedding in a house of worship in 2012, down from 2 in 5 (41%) in 2009. Additionally, more couples are opting to have a friend or family member officiate the ceremony. In 2012, 1 in 3 (33%) couples chose a friend or family member to officiate, up from 31% in 2011 and 2010, and 29% in 2009."

From a Christian standpoint, the "fading into the background" of the religious and sacred aspects of the marriage ceremony should give us pause, in part because it is associated with the largely post-modern, post-Christian worldview which is so common today. From the perspective of perhaps a large majority of conservative and evangelical churches (with which I identify), as well as the Roman Catholic Church, however, the Bible and biblical traditions still loom large in their thinking, regardless of the current post-Christian zeitgeist.

What, then, are some of the key biblical principles, either explicit and/or implicit, we can invoke to help restore the sacredness of Christian marriage? In considering these principles we should be able to appreciate why a formal and official "wedding ceremony" is a must for any Christian couple contemplating marriage. (N.B.: The words in italics in the following points are mine.)

1. One husband, one wife, for life. ". . . a man shall leave his father and mother, and be joined to his wife; and they shall become one flesh" (Genesis 2:24 NASB). The words of Jesus: "So they are no longer two, but one" (Matthew 19:6).

2. The priority of the divine- over the human aspects of marriage. Jesus' words: "Therefore what God has joined together, let man not separate" (Mark 10:9 NIV).

   The preamble to many Christian wedding ceremonies includes such words as, "Dearly Beloved, we are gathered here today in the presence of God and these witnesses, to join _______ and _______ in holy matrimony, which is commended to be honorable among all. Marriage is not to be entered into lightly, but reverently, lovingly and solemnly."

3. God's attitude toward divorce is summed up by the prophet Malachi: "'I hate divorce,' says the LORD God of Israel . . ." (2:16). In light of this, and in light of Jesus' words regarding the "grounds" for divorce--namely, "'But I tell you that anyone who divorces his wife, except for marital unfaithfulness, causes her to become an adulteress, and anyone who marries the divorced woman commits adultery'" (Matthew 5:32 NIV), we do well to adopt God's attitude regarding the sacredness of the marriage bond and the serious repercussions of treating it lightly.

   Notice that Jesus did not command divorce in the case of infidelity (or adultery); rather, he seems to be saying that if the marriage must be dissolved, then the reason should be on the grounds of infidelity, and not "falling out of love," or "irreconcilable differences," or some lesser factors such as the vicissitudes of life ("for richer, for poorer, in sickness and in health, for as long as you both shall live"). Even infidelity of either--or both--spouses can be forgiven, and reconciliation can be effected under some circumstances.

   Moreover, infidelity involves a lack of fidelity to the marriage vows generally and not just in the sexual realm. Violations to those vows which involve extreme physical and/or mental cruelty would qualify, I believe, as grounds for divorce, since they are clear violations of the vow to "love, honor, and cherish until death do you part," not to mention the "Golden Rule" of Jesus: "'. . . do to others what you would have them do to you, for this sums up the Law and the Prophets'” (Matthew 7:12).

4. The seriousness with which marriage was treated, generally speaking, in both Testaments. Besides important and very practical considerations involving the exchange of the "bride price" and dowry, the engagement of a couple made the marriage virtually a "done deal" in ancient Hebrew culture. Joseph's betrothal to Mary, for example, wasn't the kind of thing one backed out of easily. That is why Joseph decided to break off the engagement on the down-low, since he assumed that his fiancé had either betrayed him or had been raped, which was grounds for a "divorce" prior to marriage.

5. The very public and festive occasion, which today we call the reception, could be a very extravagant, lavish, and lengthy affair, not just an afternoon-to-evening affair, which is quite evident in the New Testament writings (see, for example, the parable of the foolish and wise virgins in Matthew 25:1 ff.). Jesus' very first miracle occurred at just such an affair, where he turned water into wine. Simply put, a wedding ceremony was a very public event which had its own unique protocol and customs, and was never taken lightly by either family.

In conclusion, even in the 21st century, marriage in most developed nations involves a legal contract which cannot be broken easily or with impunity. Because divorce can be such an emotionally wrenching experience for both spouses and their children, and because a burgeoning divorce rate has horrendous societal consequences as well, marriage is treated as a serious rite, despite the existence of quickie Las Vegas weddings and no-fault divorce. Since marriage is still considered today an institution with legal, moral, and even spiritual dimensions and ramifications, why would a Christian, under normal circumstances, even entertain the notion of a quick and easy marriage ceremony?

The basis for a marriage ceremony is the elevation that it grants the parties. In Paul's day, for example, only the elite could actually "marry" in the sense we have today. Sarah Ruden writes:

But for the polytheistic ancients, marriage was not as straightforward a matter. Slaves could not be legally married as free people were, but many had long-term unions that got some recognition, and raised their children together. Freedmen on average must have had less formal setups than the freeborn, since many of these setups started in slavery. In Latin the same slang, “tent-mate” and “shacking up” (literally, “tenting together”), could apply. For aristocratic Romans, the nobility’s separate legal history, along with large dowries, and ceremonies no one else went through, set their marriages apart. Even the Latin words for marriage, husband, and wife are not completely the same across different levels of privilege: uxor, for example, for “wife,” applies mainly to the upper classes; conjunx, on the other hand, can mean a wife, fiancée, concubine, or even animal’s mate, so of course it applies all over the place.

She continues by saying that marriage, as you define it, was more of an agreement than a ceremony. She writes:

What is more, the ordinary type of Roman marriage was legally defined by consent to be married, which made getting a divorce easy for either party: a husband or wife had only to make known the wish not to be married anymore; and divorce, it appears, was common during the empire. A stricter type of marriage was available, but it was unpopular. This, then, was the array of committed sexual unions allowed among the Greeks and Romans.

Against this basis, she argues that for Paul, it was an elevation of the status of the individual that marriage would be "held in high esteem by all"

In 1 Corinthians 7 (see my discussion of Christian marriage in chapter 4 ) Paul lays down the law for Christians and gives his rationales— partly because, I think, existing laws and customs were too loose, yet nobody in this world had thought much about them.

Ruden, Sarah (2010-02-10). Paul Among the People: The Apostle Reinterpreted and Reimagined in His Own Time (Kindle Locations 355-367). The Doubleday Religious Publishing Group. Kindle Edition.