There is only one question about the Genesis account that is more annoying than this one and that would be "Did Adam have a navel?"
Adam was not born, and therefore had no umbilical cord. He was formed from the dust of the ground (Gen 2:7), therefore he would not have had a navel.
Having put that one to bed, let's now assess the merits of the question in front of us.
Cain's wife is only a problem to either the casual reader or the unbeliever looking for problems.
The Bible says God made Adam, then Eve and that everyone else descended from them. The Bible makes no mention of God 'making' a wife for Cain – so where did she come from?
Adam lived 930 years (Gen.5:5). Adam fathered "sons and daughters"(Gen.5:4).
Adam was 130 years old when he fathered his third son, Seth; Cain having been born before this.
The Jewish historian Josephus claims that Adam and Eve had thirty-three sons, and twenty-three daughters (Antiquities of the Jews chapter 2). Josephus claims that these figures were traditional, but one thing is for sure, that Adam fathered daughters who are not mentioned by name in the Bible.
Incest?
The obvious answer to our question is that Cain married a sister – but we struggle with that because in 21st century England we don't marry our sisters.
The prohibition of incest was not brought in until hundreds of years later (Lev 18:9, & 20:17). In fact we know that Abraham married his half-sister (Gen.20:12). If we understand the Bible correctly the corruption in mankind, particularly in what we would now call the genome has increased since Adam's time (Rom.8:20-23), so not marrying for genetic reasons was irrelevant. Besides all this there were only near relatives to marry!
So Cain is born before Adam is 130 and Adam goes on fathering children for over 800 years. Realistically, Cain may well have had a sister that was a year or two younger than him, but even if she was one hundred years younger it would still have been no different to some of the relative age differences with which people marry now.
Some people get all worked up about the fact that Cain moved to the land of Nod. We have no idea where this land was, and in fact its name just means 'wandering', which may infer that Cain was nomadic or just lived his life wandering all over. It wouldn't be that Cain moved to Nod and found a wife there – either he went back home to collect a wife, or one went out to meet him. Either way, the idea that a woman had to pop-up from somewhere else is totally unnecessary.
It is important that the great instruction that God had given mankind was to be fruitful and multiply (Gen 1:28). For Adam and Eve's offspring that meant either brother mating with sister or possibly a niece. Without our centuries of baggage this wasn't 'gross' it was just obedience to God's command.
When Eve became Adam's wife having been created from Adam, she was called ishshah (Hebrew) which is the word for "woman/wife/female" and it means "from man." It is a derivation of the Hebrew words 'iysh (pronounced: eesh) and enowsh, which both mean "man."
This one, at last, is bone of my bone, and flesh of my flesh; this one will be called woman [ishshah], for she was taken from man [iysh]. Gen 2:23 HCSB
There is therefore some argument to say when Cain takes a wife [ishshah] he is also taking a woman who is 'from Adam' – a descendant of Adam, Cain's sister! Certainly for those who read Hebrew the wording conveys a little more than the English translation and causes less difficulty for them.
Monkey Business The State of Tennessee v. Scopes (1925) is a very famous trial that is often referred to as the Scopes Monkey Trial because it was about the teaching of Evolution in School. The Biology teacher who was the subject of the case was called Scopes, and cross examination famously included the question 'did you ever discover where Cain got his wife?' Carl Sagan included it in his book and the subsequent movie "Contact" and it has been widely discussed –especially where sceptics have sought to find inaccuracy in the Genesis account. When people want the Bible to be wrong, they look for anything that might undermine it. In reality this of all questions was an easy one to answer and shouldn't have been a problem during that trial. As it was, the respondent said that he didn't know.
The Bible is not exclusively a genealogical record, neither is it purely history and it certainly isn't science. There is a definite and single purpose for which the Bible was written -
These are written so that you may believe Jesus is the Messiah, the Son of God, and by believing you may have life in His name. John 20:31 HCSB
The account of Adam is there to help us recognise that God is creator and that we should worship Him as such (the same theme is seen towards the end of the Bible in Revelation 10).
We also have the account of Adam so that we can see that the world was made perfect by God – and so were we. The trouble, suffering, pain and tears of this world are not God's creation or plan, but the consequences of our sin and failure.
Just as sin entered the world through one man, and death through sin, in this way death spread to all men, because all sinned. Rom 5:12 HCSB
Since Adam was the head of the human race, when he fell we who were his unborn descendants also became corrupted. Thus, we are all separated from God. The final consequence of sin would be separation from God in our sinful state forever. However, the good news is that there is a way for us to return to God. God provided the solution—a way to deliver man from his corruption. Paul explains that God provided another Adam. The Son of God became a man—a perfect Man—yet still our relation. He is called "the last Adam" (1 Corinthians 15:45) because is God's final perfect Adam, the progenitor of a new race. He became the new head and, because He was sinless, was able to pay the penalty for sin.
For since death came through a man, the resurrection of the dead also comes through a man. For just as in Adam all die, so also in Christ all will be made alive. 1 Cor 15:21-22 HCSB
The issue is not about Cain, from whom we learn so much about how sin can dominate man in only one generation, nor is it about his unnamed wife, but it is all about the trail through the scriptures that leads to the cross and the offer of peace between God and man.
We lost our home in Paradise (or Eden) when sin separated us from God, and for Cain and his wife their wandering didn't allow them to put down any roots to feel like they had a home anywhere.
Those who have faith in Jesus 'now aspire to a better land—a heavenly one' Heb 11:16 HCSB because we are wandering in pilgrimage through this life and our ' hearts are set on pilgrimage'. Ps 84:5 HCSB
In Christ we will eventually inherit a new Eden, a permanent paradise which will have no more failure, pain, tears or even darkness. In the meantime, we are not diverted into writing our PhD's on Cain's wife, instead we are spending our time developing relationship with Jesus of Nazareth, the second Adam.