What are other explanations for Malachi 4:5-6? The LDS church believes the prophecy in Malachi 4:5-6 (KJV) has been fulfilled, and those verses are often cited while explaining why they're so interested in genealogy.

What other explanations exist for this prophecy? What do other denominations think it means that Elijah will "turn the hearts of fathers to their children and the hearts of children to their fathers?"
The Bible teaches that the Spirit of Elijah would be sent to the earth a total of 5 times (5 is the number of grace1). By Spirit of Elijah, I mean God's spirit anointing a man to bring a message, in the same way that the first Elijah was anointed (a straight shooter, hard hitter, come out of the wilderness, etc).

First, Elijah Himself

An examination of Elijah's traits may be beyond the scope of this question. If requested, I can revisit later.

Second - Elisha


  II Kings 2:9 And it came to pass, when they were gone over, that
  Elijah said unto Elisha, Ask what I shall do for thee, before I be
  taken away from thee. And Elisha said, I pray thee, let a double
  portion of thy spirit be upon me.
  
  II Kings 2:15 And when the sons of the prophets which were to view at
  Jericho saw him, they said, The spirit of Elijah doth rest on Elisha.
  And they came to meet him, and bowed themselves to the ground before
  him.


Third - John the Baptist (Forerunner to Jesus' First Coming)


  Malachi 3:1 Behold, I will send my messenger, and he shall prepare the
  way before me: and the Lord, whom ye seek, shall suddenly come to his
  temple, even the messenger of the covenant, whom ye delight in:
  behold, he shall come, saith the LORD of hosts.
  
  Luke 1:17 And he shall go before him in the spirit and power of Elias,
  to turn the hearts of the fathers to the children, and the disobedient
  to the wisdom of the just; to make ready a people prepared for the
  Lord. 
  
  Matthew 7:11-13 And Jesus answered and said unto them, Elias truly
  shall first come, and restore all things. But I say unto you, That
  Elias is come already, and they knew him not, but have done unto him
  whatsoever they listed. Likewise shall also the Son of man suffer of
  them. Then the disciples understood that he spake unto them of John the Baptist. 


Fourth - Forerunner to Jesus' Second Coming

Reading Malachi 3 as referring to John the Baptist's fore-running of Jesus' first coming, Malachi 4 can be read as another fore-runner preparing the way for Jesus' second coming. This man will turn the hearts of the children (the believer's of today) to the original faith preached by the early church apostles (fathers), just as John turned the hearts of the fathers of Israel to the "children" that received his message of the coming Christ. Malachi 4:5 predicts that this messenger will come before the great and dreadful day of the Lord, and if his message is rejected, the earth will be smitten with a curse.

Luke 1:17 specifically states that John would turn the hearts of the fathers to the children (Jesus' first coming), but does not include the Malachi 4:5 reference to turning the hearts of the children to the fathers (Jesus' second coming). This is similar to how Jesus, in the synagogue, began to read from Isaiah 61:1-2, but stopped halfway through verse 2 before he got to "and the day of vengeance of our God". He would fulfill that part of that verse at his second coming, but not his first.

Fifth - One of the Two Witnesses to Israel


  REVELATION 11:3 And I will give power unto my two witnesses, and they
  shall prophesy a thousand two hundred and threescore days, clothed in
  sackcloth.


See my response to this related question: Who Are the Two Witnesses? 

To briefly summarize that more detailed response, the characteristics of the two witnesses are so similar to Moses and Elijah that we can conclude that the anointing of the two witnesses will be the same that was with Moses and Elijah. This is the fifth and final time that the spirit and power of Elijah will be manifest on earth.



1 See EW Bullinger's Number in Scripture, on the number five.