I was once informed by some LDS missionaries that other churches to them are the church of Satan? Is this an LDS doctrine or the view of some members?
Yes and no.
The LDS believe they are
the true Church of Jesus Christ, which was lost through apostasy, was brought back as it originally existed when organized by Jesus Christ 1
1 Nephi 13:1-9 mentions a great and abominable church and LDS manuals explain this with the following commentary:
“In relation to the kingdom of God, the devil always sets up his kingdom at the very same time in opposition to God” (Joseph Smith, in History of the Church, 6:364).
Elder Bruce R. McConkie (1915–85) of the Quorum of the Twelve Apostles defined the great and abominable church: “The titles church of the devil and great and abominable church are used to identify all … organizations of whatever name or nature—whether political, philosophical, educational, economic, social, fraternal, civic, or religious—which are designed to take men on a course that leads away from God and his laws and thus from salvation in the kingdom of God” (Mormon Doctrine, 2nd ed. , 137–38).
One commentator explained that the great and abominable church consists of more than one entity:
“Actually, no single known historical church, denomination, or set of believers meets all the requirements for the great and abominable church: it must have formed among the Gentiles; ... No single denomination or system of beliefs fits the entire description. Rather, the role of Babylon has been played by many different agencies, ideologies, and churches in many different times. …
(Stephen E. Robinson, “Warring against the Saints of God,” Ensign, Jan. 1988, 38–39).2
While the LDS believe they are the true restored church they believe other religions and religious leaders have bits of the truth and were often important in the work of the restoration.
Some leaders mentioned in Preach My Gospel (the LDS missionary teaching manual) are: John Wycliffe, Martin Luther, William Tyndale, John Calvin, Buddha, Confucius, and Mohammed.3
A principal teaching is a respect for other religions and beliefs:
I believe that we owe respect to all churches and organizations that lead men to act more righteously than they otherwise might, even if they don’t hold the keys of salvation and even if there is much error in their teachings4
The great religious leaders of the world such as Muhammad, Confucius, and the Reformers, as well as philosophers including Socrates, Plato, and others, received a portion of God’s light. Moral truths were given to them by God to enlighten whole nations and to bring a higher level of understanding to individuals . . .
Consistent with these truths, we believe that God has given and will give to all peoples sufficient knowledge to help them on their way to eternal salvation, either in this life or in the life to come . . .
Our message therefore is one of special love and concern for the eternal welfare of all men and women, regardless of religious belief, race, or nationality, knowing that we are truly brothers and sisters because we are sons and daughters of the same Eternal Father.5
13 We believe in being honest, true, chaste, benevolent, virtuous, and in doing good to all men; indeed, we may say that we follow the admonition of Paul—We believe all things, we hope all things, we have endured many things, and hope to be able to endure all things. If there is anything virtuous, lovely, or of good report or praiseworthy, we seek after these things.
No, Mormons do not really believe that. Not like that. It sounds like those missionaries may have been either a bit zealous or oversimplified and overgeneralized the vision found in 1 Nephi 13-14:
5 And the angel said unto me: Behold the formation of a church which is most abominable above all other churches, which slayeth the saints of God, yea, and tortureth them and bindeth them down, and yoketh them with a yoke of iron, and bringeth them down into captivity.
6 And it came to pass that I beheld this great and abominable church; and I saw the devil that he was the founder of it.
It goes on to explain that "after [the Bible] hath gone forth through the hands of the great and abominable church, that there are many plain and precious things taken away from the book" (and Mormons do believe that the Bible is missing many "plain and precious" truths, hence the need for the Book of Mormon). The next chapter says:
9 And it came to pass that he said unto me: Look, and behold that great and abominable church, which is the mother of abominations, whose founder is the devil.
10 And he said unto me: Behold there are save two churches only; the one is the church of the Lamb of God, and the other is the church of the devil; wherefore, whoso belongeth not to the church of the Lamb of God belongeth to that great church, which is the mother of abominations; and she is the whore of all the earth.
So this is probably the origin of what they said to you. However, the interpretation that Mormons think all other churches are of the devil is naïve. This passage only talks about two churches, not many. Further, the LDS Church acknowledges, appreciates, and cooperates with other churches that preach of God and Jesus Christ.
What the angel is telling Nephi here is that, when the Book of Mormon was coming forth and the Lord's true Church was beginning to be restored to the Earth, that there would be those who oppose it and those who join it. We have no reason to believe the vision can be interpreted this way after the beginning of the restoration of the Church, say, today's day and age. In fact, the vision Nephi had says that the numbers of the Church of the Lamb of God were few: but these days, there are over 15 million members of the LDS Church. Does that count as a "few"? Maybe, compared to the population of the world. But there's no real official interpretation of this vision. It is left for the reader to interpret as led by the Spirit.
Another perspective on this (that has already been answered incredibly well by the people above!) comes from Gordon B. Hinckley's interview with Mike Wallace on 60 Minutes in 1996. Gordon B. Hinckley was, at the time, the president of the LDS church.
The particular quote that came to mind from the interview was the following:
Mr. Wallace: “How do you view non-Mormons?”
Response: “With love and respect. I have many non-Mormon friends. I respect them. I have the greatest of admiration for them.”
Question: “Despite the fact that they haven’t really seen the light yet?”
Reply: “Yes. To anybody who is not of this Church, I say we recognize all of the virtues and the good that you have. Bring it with you and see if we might add to it.”
The source of this belief stems from a passage in 1 Nephi 14:10
And he said unto me: Behold there are save two churches only; the one is the church of the Lamb of God, and the other is the church of the devil; wherefore, whoso belongeth not to the church of the Lamb of God belongeth to that great church, which is the mother of abominations; and she is the whore of all the earth.
The passage seems to indicate that there is a true church and that all other churches are the church of Satan. This scripture has been interpreted differently across church history. At times it has been specifically attributed to the Catholic Church, or other organizations.
Another scripture that may be the source of this belief is Joseph Smith History Verse 19.
I was answered that I must join none of them, for they were all wrong; and the Personage who addressed me said that all their creeds were an abomination in his sight; that those professors were all corrupt; that: “they draw near to me with their lips, but their hearts are far from me, they teach for doctrines the commandments of men, having a form of godliness, but they deny the power thereof.”
In this passage, Joseph Smith writes that God told him to join no churches, that none of them were true. This combined with the 1 Nephi passage lead to the conclusion that if none of the churches on the earth were the church of God, and churches that are not the church of God are the Church of Satan, then all churches that are not the Church of Jesus Christ of Latter Day Saints must be the church of Satan.
This link leads to a Mormon apologist article that shows that some leaders of the Church have said that 1 Nephi 14:10 refers to a specific church, and others have said that it refers generally to all people who oppose the teachings of Jesus Christ. The Church currently does not take an official position on the issue, but more contemporary quotations generally take the point of view that other churches are not the church of the devil.
In summary, this is not a current official teaching of the LDS church, though there are doubtless members of that church that do believe that teaching.
You've had a few helpful answers already, but I'll add a couple connections to general Christian theology which may help you understand more.
Jacob was correct to pinpoint 1 Nephi 14:10 and JS:H 1:19 as the scriptures which get referenced when people (both Mormon and non-Mormon) make such claims. It's easy to see how these scriptures could be (mis-) understood that way.
But 1 Nephi 14:10 doesn't say "there are many churches: one of them is the Church of Jesus Christ of Latter-Day Saints, and the rest of them are churches of Satan." Instead it's saying "whatever associations and divisions among people there may seem to be on the surface, ultimately people are assembled into two camps: Christ's and Satan's." (Remember that the Biblical words that are translated as "church" all originally meant an assembly, a gathering-together, the literal meaning of con-gregation.)
The "church of the Lamb of God" is thus somewhat parallel to the idea in general Christian theology of the "church invisible" or some conceptions of "the communion of the saints." Claiming to be Christian, or having your name on the rolls of the institutional Church here on earth led by apostles and prophets, doesn't necessarily mean you're part of the "church of the Lamb of God." (cf. Matt 7:22.) On the other hand, there are people who are not members of the Church of Jesus Christ of Latter-day Saints - and indeed, even people who don't know Christ by name (think of the surprised righteous in the parable of the sheep and goats, Matt 25:37) - who are in Christ's camp.
The Lord's answer to Joseph Smith about other churches can be compared with what He says to Peter in Matthew 16:23, when though Peter was well-intentioned he was putting his conception of how things work ahead of God's plan. The creeds, even if written by well-intentioned men, are "an abomination" to God not necessarily because of their content, even when in error, but because they codify a human interpretation as having authority on par with or even above the revelations of God. The Lord uses sharp language in addressing that dangerous tendency, but He used even sharper language in dressing down Peter, and He clearly didn't mean that Peter was intrinsically evil (after all, this comes right after the blessing in v.16-19).