Can Latter-day Saints believe in evolution?

My short answer is yes.

Hugh Nibley lends support:

"It takes us back to the earliest drama of Adam and the animals. He lives with them on intimate terms. He must have because he called them all by name, and they were all around him in overwhelming force. He was living in another world then, and we don't know how long it lasted since "as yet the Gods had not appointed unto Adam his reckoning" (Abraham 5:13). This was before he entered with Eve into the garden and the covenant of marriage. It was the earth's turn to bring forth new types of "beasts after their kind, and cattle after their kind, and every thing that creepeth upon the earth after its kind; and the Gods saw they would obey" (Abraham 4:25). Again the moment of testing; it is as if new ideas were being tried out in the new world."

--source: http://mi.byu.edu/publications/transcripts/?id=72&cat_id=266 from the Neal A Maxwell Institute for Religious Scholarship

The length of time to create the animals of the earth could be (and based on the preponderance of evidence indicating evolution of species has taken place) long enough for animals to evolution and adapt based on natural processes. If one were to recall the commonly stated belief that extinct animals were "God's mistakes," it would be easy to reframe a mistake as a "test;" as species developed, adapted and changed to suit their environments, and as the earth itself changed over the course of time. Quite possibly the millions of years needed for those natural processes to occur. We can remember that God's time is not man's time--"in their times and in their seasons, in their minutes, in their hours, in their days, in their weeks, in their months, in their years—all these are one year with God, but not with man" (D&C 88:44).

I have in the past read other works that also lend credence to the idea that the periods of the creation allowed enough time--millions of years--before man came onto the world scene. The scriptures refer to each "day" of creation but the same could be understood as "creative periods." If I come across more evidence of this, I will edit and repost.