This is a biggie. It's really two questions in one:

(a) Do you believe in a literal Adam and Eve, and

(b) Do you believe in evolution.

Many Mormons will probably have various opinions on both of these.

The official church statement on evolution was given in 1909: (James R. Clark, Messages of the First Presidency, Vol.4, p.206)

"The Church of Jesus Christ of Latter-day Saints, basing its belief on divine revelation, ancient and modern, proclaims man to be the direct and lineal offspring of Deity. God Himself is an exalted man, perfected, enthroned, and supreme. By His almighty power He organized the earth, and all that it contains, from spirit and element, which exist co-eternally with Himself. He formed every plant that grows, and every animal that breathes, each after its own kind, spiritually and temporally -- "that which is spiritual being in the likeness of that which is temporal, and that which is temporal in the likeness of that which is spiritual." He made the tadpole and the ape, the lion and the elephant but He did not make them in His own image, nor endow them with Godlike reason and intelligence."

In other words, there is a basic difference between animal and man, that man was created as the offspring of God.

As far as Adam and Eve go, Mormons certainly believe that parts of the Bible are symbolic. Some probably believe that the story of Adam and Eve is symbolic, and some don't. As the Encyclopedia of Mormonism notes, "The scriptures tell why man was created, but they do not tell how." (Encyclopedia of Mormonism, Vol.2, EVOLUTION article.)

My own personal view is this:

I believe that evolution is a possible mechanism by which the human bodies were created, although not necessarily the actual way. However, the definite difference between us and the other animals is that we are literally spirit children of God (as per the First Presidency statement above). With that view, I believe there was a literal person, called Adam, who was the first being on this Earth to be a spirit child of God. I'm willing to accept an approximate chronology outlined by the Bible, that this first spirit child of God lived around six thousand years ago, and that the beings (whether animal-like or human-like) who may have existed on the earth prior to that were not related to God in the same way that we are. So, if anatomically modern humans preexisted Adam-Eve (or were contemporary with them), they would have an afterlife similar to that of animals. In my opinion, their freedom of choice would also be more similar to that of animals rather than that of humans.

I guess fundamental in my view is the Mormon doctrine that humans (beginning with Adam & Eve) are of "the same stuff" as God (and can become gods), whereas the animals are of "different stuff".