The short answer to this is simple: No. Many Mormons casually refer to "hell" in the same way that other Christians do, as a place of punishment where sinners are sent by a wrathful God. Even The Book of Mormon mentions hell as a place of fire and pain (1 Ne 9:10 and Helaman 6:28), a place that can be avoided by obedience to God and His commandments. But this is largely a metaphorical place. We can feel we are in "hell" even in this world because we are disobedient to God and His commandments and feel the consequences of bad decisions. We can also feel that we are in "hell" in this world if we are separated from God and His abounding love for us.
There is a second "hell" that Mormons believe in, but it is also not a place that God has created for sinners. Rather, it is a place where those who die in ignorance of Christ go because they do not have the knowledge to enter what Mormons sometimes refer to as "Spirit Paradise," the place where the righteous go after death to await their resurrection. If this sounds like a Catholic Purgatory, there are admittedly certain similarities. Mormons do temple work rather than saying prayers so that those in "Spirit Prison" can move to "Spirit Paradise" and associate with other believers. But again, Mormon theology on Spirit Prison has nothing to do with a place of fire and brimstone, except metaphorically, as spirits may feel anguish at being separated from Christ and from their loved ones who are believers.
In fact, Mormons believe that Christ Himself went to visit Spirit Paradise (D&C 76:73) during the three days after He was crucified and before he was resurrected, in order to organize missionaries to travel to Spirit Prison to convert those who had never had a chance to know of Christ. Sometimes Mormon missionaries who die on missions or who die just before going on missions are said to have been called to a different mission to preach the gospel to those on "the other side of the veil." The great work of the Millennium (the thousand years after the Second Coming of Christ), according to Brigham Young, will be temple work, continuing to do ordinances for every person who has ever lived on the earth.
But the reality is that along with universal resurrection, Mormons believe that nearly everyone is eventually given a place in one of the three heavens--or degrees of glory, the telestial kingdom, the terrestrial kingdom, and the celestial kingdom. This is one of the things that I love most about Mormonism, that we believe in God as a loving Father, eager to give as much as He can to us, His arms always outstretched. God does not punish us. We punish ourselves in being separate from Him and His Love. Christ's Atonement is infinite and includes all of us, even if those who do not accept Him, even the most wicked. All are resurrected and are given as much as they will accept of the blessings of the Atonement.
And before I get Mormons telling me I'm wrong, there is one more sense of "hell" that Mormons believe in, a place that is called "Outer Darkness." This is where the "sons of perdition" go**, those who have known Christ truly and have denied Him, as well as where Satan and his angels live who rejected Christ from the first. But within Mormonism, there is much debate about who might qualify for this place. I've heard both Cain and Judas are likely to be in Outer Darkness, but there is debate even there. There's no agreed upon list of those who are going to Outer Darkness, a place that is simply described in Mormon theology by its lack of the presence of God, Christ, or even the Holy Spirit. Rather than be a place of fire and brimstone, it seems more likely this is a place of cold and darkness, and perhaps even silence.
So, what are the three Mormon heavens like? The telestial kingdom is filled "liars, and sorcerers, and adulterers, and whoremongers, and whosever loves and makes a lie" (D&C 76: 103), with murderers and other people who were wicked in their lifetimes, but have since confessed Christ their savior, as all will at the end of days. Because God and Christ cannot visit this place due to lack of perfection, these people can only experience the presence of the Holy Spirit. But still, God seems to give them all that He can and the Doctrine and Covenants says that even this kingdom's gory "surpasses all understanding."
The terrestrial kingdom is filled with "honorable men of the earth, who were blinded by the craftiness of men" (D&C 76: 75), good people who would choose not to do all the work that is required in the celestial kingdom. They are not as "valiant" in the testimony of Christ as those in the celestial kingdom, but they "receive of the presence of the Son, but not of the fullness of the Father" (D&C 76: 77). There is a perhaps apocryphal story of Joseph Smith having said that the terrestrial kingdom was so glorious that if we had a glimpse of it, we would gladly die to get there.
The celestial kingdom is filled with "just men made perfect through Jesus" (D&C 76:69). They are those who want to spend all of their time becoming more like God, learning every detail of knowledge in every area of the universe, and going on to continue to serve others and even to have larger and larger families (D&C 76). Those in the celestial kingdom will spend time ministering to those in the terrestrial kingdom. They will spend the eternities doing the services to others which Christ demonstrated while He was on the earth.
If the Mormon idea of the celestial kingdom doesn't sound like heaven to you, well, there are plenty of Mormons who debate about how desirable it is, as well. I have thought to myself on occasion (and heard other Mormons echo this thought), maybe I wouldn't choose to be in the celestial kingdom. Maybe I'd rather have a rest from continuing to work and serve, to learn and make mistakes and grow forever.
I love the fact that Mormon doctrine denies no one resurrection, not even the worst of murderers, and I love the idea that God is so generous and loving to His children, that He wants to grant us as much of His own estate and knowledge as He possibly can. I love that our scriptures say that God's work and His glory is to "bring to pass the immortality and eternal life of man" (Moses 1:39), that is, that God is still serving us, even in His perfection. I love that Christ's infinite grace extends to all and lifts us as far as we choose to go. I admit that I am not always excited about the idea of working after I'm dead, but if I'm going to work, having my loved ones around me would make it a lot sweeter. And with a perfect, resurrected body, maybe I would have no idea what it is like anymore to be tired.