Do Mormons Worship Joseph Smith?

No. We don't worship Joseph Smith. Or Mormon, or Moroni (the guy on the Temples with the trumpet) or anyone other than Jesus Christ. Those other people are messengers. They are not even 'intermediaries'. A true messenger brings teachings from God, but then directs us to establish a direct, personal relationship with God and Jesus Christ.

God does now (and has always) used messengers to establish his Word. But all of our prayers are directed to God our Heavenly Father and closed in the name of his only intermediary, his son Jesus Christ.

With regards to the mission of Joseph Smith (and the Mormon view of what a Prophet is), consider this excerpt from an article by James Faust, a former member of the Church's First Presidency:

"As I submit to you my testimony of Joseph Smith, I acknowledge his humanness along with his great spiritual powers. He did not claim to be divine, nor a perfect man. He claimed only to be a mortal man with human feelings and imperfections, trying honestly to fulfill the divine mission given to him. He so describes himself in recorded counsel given to some of the members of the Church who had just arrived in Nauvoo on October 29, 1842. Said the Prophet, 'I told them I was but a man, and they must not expect me to be perfect; if they expected perfection from me, I should expect it from them; but if they would bear with my infirmities and the infirmities of the brethren, I would likewise bear with their infirmities.' (History of the Church, 5:181.)"I am impressed with his complete candor, for in addition to admitting his own humanness, he also recorded the declarations from the Lord which were given to him in the nature of loving reproof. . . ."While Joseph sought perfection, he did not claim perfection. If he were intending to fabricate a great falsehood or wanted to perpetrate a fraud or practice deceit, would he have been so truthful about his own humanness? His complete candor in admitting human frailties and in declaring the loving discipline of God offers powerful proof of his honesty and probity. His statements stand on more solid footing because they were declarations against human nature and admissions against self-interest."

- James E. Faust, "The Expanding Inheritance from Joseph Smith," Ensign, Nov. 1981, 76–77"