The first statement that anyone should know about in relation to Islam, and world religions in general, is the First Presidency Statement from 1978:
The great religious leaders of the world such as Mohammed, 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. (First Presidency message, 15 Feb 1978)
Many very positive statements about Islam came in the early days of the Church. In 1855 George A. Smith stated
...this Mahometan [Muslim] race, this dominant power of the 7th and 8th centuries, were the descendants of Abraham, which Mahometan records show in a straight-forward genealogy, from the family of Mahomet [Muhammad] direct to that of Abraham, through the loins of Ishmael, the son of Abraham; and in this dominion there certainly was a recognition of the dominion of the sons of Abraham. (Journal of Discourses 3:34)
It is also worth noting that in Genesis 21:13 Abraham was promised that Ishmael would also be made a great nation.Howard W. Hunter said, "The Church has an interest in all of Abraham's descendants, and we should remember that the history of the Arabs goes back to Abraham through his son Ishmael." ("All Are Alike unto God," 1979 Devotional Speeches of the Year, Provo: Brigham Young University Press, 1980, pp. 35-36).
George A. Smith also said
Parley P. Pratt stated in the same conference in 1855:
...there was nothing in [Muhammad's] religion to license iniquity or corruption; he preached the moral doctrines which the Savior taught; viz., to do as they would be done by; and not to do violence to any man, nor to render evil for evil; and to worship one God. (Journal of Discourses :31)
Though Mahometan institutions are corrupt enough, and need reforming by the gospel, I am inclined to think, upon the whole, leaving out the corruptions of men in high places among them, that they have better morals and better institutions than many Christian nations; and in many localities there have been high standards of morals. (Journal of Discourses 3:41)
There are many more statements about Islam and the Church. Of course we do not believe that Islam has the fulness of the gospel, but to believe that Islam is completely wrong is also a mistake. There are major doctrinal differences, but I think more tolerance and openness are in order- there are enough people criticizing Islam without us adding to the chorus.
If you are specifically interested in the Arab-Israeli conflict and LDS views on it, see this Ensign article.