When I was a Mormon, I was taught that Joseph Smith had only one wife, Emma Hale Smith. I have since learned that Joseph Smith married over two dozen women — and apparently consummated some of those marriages.

To date, no proof exists to substantiate the claims of some of the children of his wives that they were descended from Joseph Smith, except those children by Emma Hale Smth.
However, if no children were conceived as a result of those polygamous marriages, they were considered whoredoms by the Book of Mormon which Joseph Smith produced.
See:
Jacob Chapter 2
23 But the word of God burdens me because of your grosser crimes. For behold, thus saith the Lord: This people begin to wax in iniquity; they understand not the scriptures, for they seek to excuse themselves in committing whoredoms, because of the things which were written concerning David, and Solomon his son.
24 Behold, David and Solomon truly had many wives and concubines, which thing was abominable before me, saith the Lord.
25 Wherefore, thus saith the Lord, I have led this people forth out of the land of Jerusalem, by the power of mine arm, that I might raise up unto me a righteous branch from the fruit of the loins of Joseph.
26 Wherefore, I the Lord God will not suffer that this people shall do like unto them of old.
27 Wherefore, my brethren, hear me, and hearken to the word of the Lord: For there shall not any man among you have save it be one wife; and concubines he shall have none;
28 For I, the Lord God, delight in the chastity of women. And whoredoms are an abomination before me; thus saith the Lord of Hosts.
29 Wherefore, this people shall keep my commandments, saith the Lord of Hosts, or cursed be the land for their sakes.
30 For if I will, saith the Lord of Hosts, raise up seed unto me, I will command my people; otherwise they shall hearken unto these things. (emphasis added.)
For more information, see The Mormon Mirage 3rd Edition:  A Former Member Looks at the Mormon Church Today(Zondervan, 2009). Also available as an audiobook and as an expanded-text E-book for Nook, Kindle and other reading devices.