Throughout Joseph Smith's time as the Prophet of the Mormon Church, he denied again and again that he or anyone else was living polygamously. 

August, 1835

In the 1835 edition of the Doctrine and Covenants, section 101 we read the following:

Section 101
MARRIAGE.

1 According to the custom of all civilized nations, marriage is regulated by laws and ceremonies: therefore we believe, that all marriages in this church of Christ of Latter Day Saints, should be solemnized in a public meeting, or feast, prepared for that purpose: and that the solemnization should be performed by a presiding high priest, high priest, bishop, elder, or priest, not even prohibiting those persons who are desirous to get married, of being married by other authority. We believe that it is not right to prohibit members of this church from marrying out of the church, if it be their determination so todo, but such persons will be considered weak in the faith of our Lord and Savior Jesus Christ.

2 Marriage should be celebrated with prayer and thanksgiving; and at the solemnization, the persons to be married, standing together, the man on the right, and the woman on the left, shall be addressed, by the person officiating, as he shall be directed by the holy Spirit; and if there be no legal objections, he shall say, calling each by their names: “You both mutually agree to be each other’s companion, husband and wife, observing the legal rights belonging to this condition; that is, keeping yourselves wholly for each other, and from all others, during your lives.” And when they have answered “Yes,” he shall pronounce them “husband and wife” in the name of the Lord Jesus Christ, and by virtue of the laws of the country and authority vested in him: “may God add his blessings and keep you to fulfill your covenants from henceforth and forever. Amen.”

3 The clerk of every church should keep a record of all marriages, solemnized in his branch.

4 All legal contracts of marriage made before a person is baptized into this church, should be held sacred and fulfilled. Inasmuch as this church of Christ has been reproached withthe crime of fornication, and polygamy: we declare that we believe, that one man should have one wife; and one woman,but one husband, except in case of death, when either is atliberty to marry again. It is not right to persuade a womanto be baptized contrary to the will of her husband, neither is itlawful to influence her to leave her husband. All children arebound by law to obey their parents; and to influence them toembrace any religious faith, or be baptized, or leave their parents without their consent, is unlawful and unjust. We believe that all persons who exercise control over their fellow beings, and prevent them from embracing the truth, will have to answer for that sin.

[Section 101, 1835]

May 5, 1838

On May 5, 1838 (after Joseph had been married to Fanny Alger), Joseph Smith denied polygamy. In the History of the Church vol. 3, chap. 3 it reads:

Question: “Do the Mormons believe in having more wives than one?”

Joseph Smith: “No, not at the same time. But they believe that if their companion dies, they have a right to marry again. But we do disapprove of the custom, which has gained in the world, and has been practiced among us, to our great mortification, in marrying in five or six weeks, or even in two or three months, after the death of their companion. We believe that due respect ought to be had to the memory of the dead, and the feelings of both friends and children.

[Elder's Journal, July 1838]

May 26, 1844

From The History of the Church volume 7, Joseph's most famous denial of polygamy is recorded as follows:

"I had not been married scarcely five minutes, and made one proclamation of the Gospel, before it was reported that I had seven wives. I mean to live and proclaim the truth as long as I can.

This new holy prophet [William Law] has gone to Carthage and swore that I had told him that I was guilty of adultery. This spiritual wifeism! Why, a man dares not speak or wink, for fear of being accused of this...

A man asked me whether the commandment was given that a man may have seven wives; and now the new prophet has charged me with adultery. I never had any fuss with these men until that Female Relief Society brought out the paper against adulterers and adulteresses. [To learn more, click here.]

Dr. Goforth was invited into the Laws' clique, and Dr. Foster and the clique were dissatisfied with that document,[2] and they rush away and leave the Church, and conspire to take away my life; and because I will not countenance such wickedness,[3] they proclaim that I have been a true prophet, but that I am now a fallen prophet.

[Joseph H.] Jackson[4] has committed murder, robbery, and perjury; and I can prove it by half-a-dozen witnesses. Jackson got up and said—"By God, he is innocent," and now swears that I am guilty. He threatened my life.

There is another Law, not the prophet, who was cashiered for dishonesty and robbing the government. Wilson Law also swears that I told him I was guilty of adultery. Brother Jonathan Dunham can swear to the contrary. I have been chained. I have rattled chains before in a dungeon for the truth's sake. I am innocent of all these charges, and you can bear witness of my innocence, for you know me yourselves.

When I love the poor, I ask no favors of the rich. I can go to the cross—I can lay down my life; but don't forsake me. I want the friendship of my brethren.—Let us teach the things of Jesus Christ. Pride goes before destruction, and a haughty spirit before a downfall.

Be meek and lowly, upright and pure; render good for evil. If you bring on yourselves your own destruction, I will complain. It is not right for a man to bare down his neck to the oppressor always. Be humble and patient in all circumstances of life; we shall then triumph more gloriously. What a thing it is for a man to be accused of committing adultery, and having seven wives, when I can only find one.

I am the same man, and as innocent as I was fourteen years ago; and I can prove them all perjurers. I labored with these apostates myself until I was out of all manner of patience; and then I sent my brother Hyrum, whom they virtually kicked out of doors.[5]