Krishna had 16108 wives! We would talk about 16000 first--Krishna's 16000 wives is a much talked about topic and people often look down upon this in their ignorance of context; same stands true about Rasa-lila which we would discuss about in another thread. Those who are devoid of devotion are very quick to raise a question about this without at first reading the sources. Half knowledge is dangerous, especially in absence of devotion; Krishna is God beyond all forms and his body is divine and he can have as many wives as he wishes to have--but he gave a reasonable example by marrying those 16000 women who were suffering in the harem of Bhaumasura.
Bhaumasura was also known as Narakasura. He was son of Bhumi(earth-elemental) and that is why he was called 'Bhaumasura.' When he plundered through world he had abducted sixteen thousand young delectable women for himself and now they were part of his harem. Some of them were wives or daughters of kings who were killed by him in various wars, others daughters of sages and rest of them just beautiful women he saw and desired to possess.
When Krishna killed Bhaumasura to help Indra(King of Swargaloka)--as he entered into the Pragjyotishpura--the elegant, prosperous and affluent city of Narakasura; these sixteen thousand women, as soon as they saw him, fell in love with him and each one of them thought in her mind "I give my heart, my soul to him; let him become my husband!Let Bramha grant this one absolute wish of mine." Knowing what they wanted, knowing they had nowhere else to turn, Krishna had them clothed in finery, adorned with the finest ornaments in Narka's treasury, and sent them home to Dwarka in golden palanquins.
Krishna married them all on the same day. He gave each of them a palace, and he lived with every one of them, assuming different(but identical) bodies for each one of them. Every woman had her own Krishna with her all the times and they lived in a condition of permanent ecstasy. It would sound ridiculous for a normal human being, but there are many accounts of similar assuming of forms by Krishna in Bhagvata Purana. The God which has become Narayana and Vishnu in so many universes can assume as many similar forms as he wants to. Read the story of Bramha's abducting cowherd boys for a more clear picture.
Part of the passages have been taken from Ramesh Menon's literary rendering of Bhagvata Purana Canto 10, Chapter--Slaying of Naraka.
Annotation From Caitanya Caritamrita:
CC Madhya 20.165: "The Supreme Personality of Godhead exists in three principal forms — svayaḿ-rūpa, tad-ekātma-rūpa and āveśa-rūpa.
CC Madhya 20.166: "The original form of the Lord [svayaḿ-rūpa] is exhibited in two forms — svayaḿ-rūpa and svayaḿ-prakāśa. In His original form as svayaḿ-rūpa,Kṛṣṇa is observed as a cowherd boy in Vṛndāvana.
CC Madhya 20.167: "In His original form, Kṛṣṇa manifests Himself in two features — prābhava and vaibhava. He expands His one original form into many, as He did during the rāsa-līlā dance.
CC Madhya 20.168: "When the Lord married 16,108 wives at Dvārakā, He expanded Himself into many forms. These expansions and the expansions at the rāsa dance are called prābhava-prakāśa, according to the directions of revealed scriptures.
CC Madhya 20.169: "The prābhava-prakāśa expansions of Lord Kṛṣṇa are not like the expansions of the sage Saubhari. Had they been so, Nārada would not have been astonished to see them.
CC Madhya 20.170: "'It is astounding that Lord Śrī Kṛṣṇa, who is one without a second, expanded Himself in sixteen thousand similar forms to marry sixteen thousand queens in their respective homes.'
CC Madhya 20.171: "If one form or feature is differently manifested according to different emotional features, it is called vaibhava-prakāśa.
CC Madhya 20.172: "When the Lord expands Himself in innumerable forms, there is no difference in the forms, but due to different features, bodily colors and weapons, the names are different.
CC Madhya 20.173: "'In different Vedic scriptures, there are prescribed rules and regulative principles for worshiping different types of forms. When one is purified by these rules and regulations, he worships You, the Supreme Personality of Godhead. Although manifested in many forms, You are one.