One of my favorite LDS-authored hymns is William Clayton's 1846 composition "Come, Come Ye Saints" (initially titled "All is Well"), written en route from Nauvoo to Utah. The following, I think, is one of the better performances available on YouTube, since the Mormon Tabernacle Choir rendition is too... choir-y... for my taste:
Personally, I think it's beautiful, both musically and lyrically. (And have I mentioned that I'm a total sucker for the word "wend"?) It's also one of the few LDS hymns that's been adapted and adopted by Protestants. A while back, a woman named Avis B. Christiansen modified the third verse slightly to make it more suitable for Protestant audiences; I'm told that it's appeared in a United Church of Christ hymnal.