What roles do faith and works play in the LDS/Mormon understanding of salvation? A primary point in the Reformation was the issue of sola fide--the position that salvation is by faith alone, apart from works.  This was to distinguish the position that works were necessary for salvation.

In LDS/Mormon theology, what is the position on faith and works in salvation?  Is it sola fide or something else?
As consolidated as I can make this: Mormons believe that we are saved from death by the grace of Christ, that faith is demonstrated by good works, and that these combined result in salvation.
Interestingly, I've often heard it accused that the LDS doctrine is that works save. I've come to find this is not true, for while works are required for salvation, no amount of good deeds will actually redeem us from spiritual death.
The actual LDS doctrine is that only by the grace and power which is in Christ can man be saved, after all we can do. Nephi wrote it:

23 For we labor diligently to write, to persuade our children, and also our brethren, to believe in Christ, and to be reconciled to God; for we know that it is by grace that we are saved, after all we can do.

Jacob, a prophet in the Book of Mormon, makes this clear too:

11 Wherefore, beloved brethren, be reconciled unto him through the atonement of Christ, his Only Begotten Son, and ye may obtain a resurrection, according to the power of the resurrection which is in Christ, and be presented as the first-fruits of Christ unto God, having faith, and obtained a good hope of glory in him before he manifesteth himself in the flesh.

Ammon, a missionary in the Book of Mormon, teaches the relationship between faith and works:

18 Thus God has provided a means that man, through faith, might work mighty miracles; therefore he becometh a great benefit to his fellow beings.

Evidently by our faith we are expected to bring about works, which do not save us, but which are of benefit to our neighbors, and that is a quality of Christ.
Alma also makes this clear:

24 And see that ye have faith, hope, and charity, and then ye will always abound in good works.

And earlier in Chapter 5, Alma is exhorting the people of Zarahemla to follow Christ:

16 I say unto you, can you imagine to yourselves that ye hear the voice of the Lord, saying unto you, in that day: Come unto me ye blessed, for behold, your works have been the works of righteousness upon the face of the earth?
17 Or do ye imagine to yourselves that ye can lie unto the Lord in that day, and say—Lord, our works have been righteous works upon the face of the earth—and that he will save you?
...  41 Therefore, if a man bringeth forth good works he hearkeneth unto the voice of the good shepherd, and he doth follow him; but whosoever bringeth forth evil works, the same becometh a child of the devil, for he hearkeneth unto his voice, and doth follow him.

Our works reflect who we follow.
Hence, Christ saves, not faith. By our faith in Christ comes good works, and although works do not save, our faith in Christ (and all that implies) qualifies us for salvation.
For further reading:

http://www.lds.org/plan/jesus-christ-is-the-way
http://mormon.org/jesus-christ/
http://www.lds.org/ensign/1998/05/have-you-been-saved