This page will not give the story of Krsna marrying 16,108 wives, but we will only attempt to explain but a few of the dharmic reasons why Krsna married so many wives.
One reason why is because in His previous incarnation as Lord Sri Ram-Candra He had taken the Eka-Patni vrata. This vow was to only take one wife and never to marry or remarry again in that lifetime. Yet, in that incarnation many of the brahmans and sages knew that Ram-Raj was none other than the Supreme Personality of Godhead Himself. He was so beautiful, effulgent, valiant, powerful, etc. Full of all 6-Opulences, Bhagavan. As such, thousands of sages and brahmans prayed that in His next incarnation they could take birth as qualified princesses and be able to become His wives in His next incarnation.
Another reason is that all souls are prakriti, female, by nature, and Krsna is the Supreme Purush, or Supreme Male. Thus, by our eternal spiritual nature we are natually inclined toward the position of wife and God as our husband.
One of the most intimate services one can render to a man is that of conjugal relationship. We, the souls, which are female by nature, are to Love God, and the highest expression of that love is as a Lover. To Love God, the Supreme Male, in the form of a female lover. Thus, to become God's wife is one of the highest means of allowing souls to love God in such an intimate and conjugal way.
When God thus appears on this Earth planet it is natural that He satisfy the desires of so many of His devotees. So many souls desired to render service in the conjugal loving mood unto Him, it is out of His kind mercy that He arranges to marry 16,108 wives.
Another, more mundane reason, however, still a social religous principle (dharma) is because He was able to protect so many women, and these women needed such protection.
Now we come to the real point of this page, as it is writen in context of trying to explain a dharmic reason as it would apply to us in our own lives and society. The religious idea of men taking more than one wife is actually for this purpose, to provide a means that so many women may get proper religious protection by a responsible man.
Krsna originally married Rukmini, His first wife, then Satyabhauma, then Kalindi-Yamuna and another 5 wives - 8 in total. Then he married another 16100 all at one time. How that was so is an interesting story, but we will not give the full story here.
In brief: There was a demoniac king named Bhaumasura who was found of young unwed girls. He was a powerful demon. He went from one state to the next, entered the palace and kidnaped the princesses (daughters) of the kings. One palace after another, he would kidnap the young girls, take the girls to a mountain cave and lock them up in that cave. Yet, he had not touched the girls or violated them. He was simply collecting as many as he could, thinking that later he would return and enjoy them all, living in the company of so many young attractive princesses.
Krsna heard about this and understood that no one else was able to defeat this Bhaumasura, except Lord Krsna. So, Krsna fought and defeated this Bhaumasura, killing him. He then went to the cave to rescue the princesses. There he found 16,100 of the most attractive young girls. When they saw Krsna enter the cave, they realized that He was the Supreme Male, the most handsome man, and so powerful, He could defeat all the powerful demoniac kings. Their hearts were taken by Him. And, they had been kidnapped. No other prince would want them, they were like spoiled goods. Yet, they had not been violated, they knew that Krsna would know this, so they all fell at Krsna's feet and begged Him to accept all 16,100 of them as His wives, because if He would not, then no one else would take them. So, they pleaded for His mercy. They all required His protection.
So, Krsna had no other choice but to accept. He married all of them at one time, bringing the total number of wives to 16,108.
Some people say that there were only 16,000 or 16,008 wives total. In fact I have seen one rascal take the great work of Srila Prabhupad, his translations of Srimad Bhagavatam, and re-write the purports and re-arrange the verses. He admits living in the ISKCON temples, taking initation from Suhotra Swami. He also admits that his Srimad Bhagavatam is based on the work of A. C. Bhaktivedanta Swami Prabhupad. But, he changes what Srila Prabhupad wrote. Thus this rascal thinks himself greater then Srila Prabhupad and the previous acharyas.
This rascal puts forth the argument that there is a verse in Srimad Bhagavatam that mentions (in Sanskrit) sixteen and more thousand. But, some wrongly read or translated that as sixteen thousand, leaving out the "and more". There are other 'gurus' in India who translate it this way, that there were only 16000 princes stollen by Bhaumasura. However, Srila Prabhupad translates the Sanskrit as 16 and more 1000. And, Srila Prabhupad quotes Srila Sridhar Swami who says that in other puranas it is specifically stated as 16100 wives. Thus, the acharyas in our line teach that there were 16100 wives total whom he married wholesale at one time, plus the 8 first wives, for a total of 16108. Those who say it is 16008 are mistaken.
This rascal thinks he is greater than Srila Prabhupad and the previous acharyas in our line as he makes an issue of this, that according to his ignorance there is only 16008. On the surface it may seem to be a minor detail. But, it actually shows how rascal these cheaters are. He is using Srila Prabhupad's translation, using Prabhupad's hard work, for his own material gain for fame and adoration. He wants followers, he wants their worship. He wants to be guru. But, he is wrongly thinking that if he presents the same thing Srila Prabhupad presented, then why come to him, better we just go to Srila Prabhupad. No, he wants his own followers, he wants that people come to him. So, he re-writes Srila Prabhupad's books and changes them, introduces differences here and there to show that he has a superior understanding so that people will think, "O' Srila Prabhupad's work was great, but this man's (rascal's) work is even greater, an improvement, let us now follow him". He is rascal.
The true quality of a guru is that he presents what his guru has taught, without changing it. Then one is qualified to teach. Otherwise, one is simply introducing chaos and misguiding the people with his own non-sense.
Well, that took us off the topic of 16,108, but it is needed in defense of the great work Srila Prabhupad has left us.