Mormons are not only taught that God was a man in the past who is now exalted, they are also taught that God is still a creature of "flesh and bone." This contrasts strongly with traditional Christian teachings that God is incorporeal and immaterial, with no relation whatsoever to physical bodies.
In some ways this particular Mormon teaching isn't as strange as it first appears. Although it's radically different from what Christians today are taught to believe, it wasn't too far out from mainstream Christian beliefs when Joseph Smith created Mormonism and it's fairly consistent with the depiction of God in the Old Testament, a major source of ideas and doctrines for Mormonism.
Mormon Texts on God's Physical Body of Flesh and Bones
In Doctrine and Covenants Mormons are taught:
"The Father has a body of flesh and bones as tangible as man’s; the Son also; but the Holy Ghost has not a body of flesh and bones, but is a personage of Spirit.
Were it not so, the Holy Ghost could not dwell in us. A man may receive the Holy Ghost, and it may descend upon him and not tarry with him." [D&C 130: 22-23]
The History of The Church of Jesus Christ of Latter-day Saints records Joseph Smith saying the following was revealed to him at Nauvoo, Illinois, on February 9, 1843:
"There are two kinds of beings in heaven--viz., angels, who are resurrected personages, having bodies of flesh and bones. For instance, Jesus said, "Handle me and see, for a spirit hath not flesh and bones, as ye see me have. 2nd. The spirits of just men made perfect--they who are not resurrected, but inherit the same glory."
These beliefs continue down through today. Dr. Stephen E. Robinson, a Mormon scholar and apologist, has written:
"We take this literally to mean that God has a physical image and that humanity is created in it."
Immanent vs. Transcendent Gods
A fundamental aspect of both the origin and nature of Mormonism is the idea of "restoration." Joseph Smith believed that God was giving him the responsibility of "restoring" the original, true Christianity. An important premise behind this was that there had been on true Christian church since the time of the apostles and that everything produced since then — including the New Testament — had been corrupted and was filled with errors.
In claiming that God "has a body of flesh and bones," Joseph Smith entered into a long-standing debate about the nature of God: is God immanent, transcendent, or some combination of both? transcendent God is beyond perception, independent of the universe, and wholly “other” when compared to us. An immanent God, is exists within the universe and is limited by the physical laws of the universe.
Tension between the two can be found throughout the history of Christianity and Judaism. Elements of both can be found throughout the scriptures of Christianity and Judaism. For the most part, though, the Old Testament tends to emphasize God as being immanent — a god that walks, talks, and interacts with people almost like another person. The God of the Old Testament tends to conform to the idea of an old, bearded man in the sky — a image of God that was probably consistent with most popular ideas in Joseph Smith's time and which he took to its logical conclusion.
In contrast to this, God in Christianity became much more transcendent, largely due to the influence of Greek philosophy. Joseph Smith rejected these ideas and thus defended his idea a physical, corporeal God by arguing against the incorporation of alien elements into Christianity. This was part of his larger argument that Christianity had become corrupted and filled with errors.
Corporeal, Physical Gods Today
The idea of a God being a person with a physical form certainly hasn't disappeared, especially in popular imagination, and it probably never well. God as a wholly transcendent "other" with no relationship to humanity is difficult to relate to and difficult to maintain interest in or worship of.
This is arguably why the idea of God being incarnated in the physical form of Jesus is so appealing to Christians — it takes a distant, transcendent god and places it right in the middle of human life.
The teachings of the LDS Church takes that a step further and says that not only did Jesus have a physical body, but he still does and so does God. However, the transcendence of God in Christianity has taken a firm hold theologically, which means that Mormonism's rather extreme form of immanence appears even stranger today than it did back in Joseph Smith's time. It may contradict orthodox, traditional Christianity, but it's not entirely inconsistent with everything in Christianity's background.
Nevertheless, the fact that it contradicts traditional, mainstream Christian theology today means that you won't find Mormons discussing this belief directly with non-Mormons. When Mitt Romney talks about "God," for example, you aren't likely to hear him talk about how God has a body of flesh and bones.