One thousand, including concubines.
The Torah prohibits Israelite kings from being very ostentatious (Deuteronomy ch.17). Solomon did permit himself to do so, which was wrong, but his motivation was the desire to be seen as lavish by foreign monarchs (1 Kings 10:23) in order to attract them to the service of God. Through his vast God-given wisdom, he spoke and taught about God's creations, influencing many nations (at least temporarily) to recognize the wisdom of God. This is similar to the practice of Abraham (Genesis 21:33) and is what is meant by "And he [Solomon] spoke of the trees, from the cedars of Lebanon to the hyssop that grows on the wall; and he spoke of the animals, the birds, the insects, and the fishes. And people came from all nations to hear the wisdom of Solomon, from all kings of the earth, who had heard of his wisdom" (1 Kings 5:13-14). In this he had success (1 Kings 10:1 and 10:24), but he died too young to bring about the fruition of his grand idea (he died at the age of 52).
He had 700 official wives and 300 concubines.
According to the Bible at I Kings 11:1-7 says And King Sol′o·mon himself loved many foreign wives along with the daughter of Phar′aoh, Mo′ab·ite, Am′mon·ite, E′dom·ite, Si·do′ni·an [and] Hit′tite women, from the nations of whom Jehovah had said to the sons of Israel: "YOU must not go in among them, and they themselves should not come in among YOU; truly they will incline YOUR heart to follow their gods." It was to them that Sol′o·mon clung to love [them]. And he came to have seven hundred wives, princesses, and three hundred concubines; and his wives gradually inclined his heart". And it came about in the time of Sol′o·mon's growing old that his wives themselves had inclined his heart to follow other gods; and his heart did not prove to be complete with Jehovah his God like the heart of David his father. And Sol′o·mon began going after Ash′to·reth the goddess of the Si·do′ni·ans and after Mil′com the disgusting thing of the Am′mon·ites. And Sol′o·mon began to do what was bad in the eyes of Jehovah, and he did not follow Jehovah fully like David his father.
That is about a thousand women.