If anyone's waiting for my stunning conclusions to the Sages Trilogy, I apologize.  Quite simply, I'm sick of writing about the Sages, as I have been doing for quite a while.  So instead, we will go to the kings.  What happens to them?  They almost never appear in the games.  This has even lead to some pretty wild theories, including one that Ganondorf was the true king.  It doesn't take too much effort to see that that is false, but I will try to explain what the kings have been doing in their spare time.  Which, for the most part, is not pleasant.  After all, with Ganon lurking around, a king's life is anything but pleasant.
    
Let's start with the king in OoT.  He exists, obviously.  The closest we see of him is Ganondorf kneeling to him.  He's fairly unimportant, seeing as he doesn't find Ganondorf as a threat.  Thus, the story ignores him as a child, for he is certainly not aiding your quest in any way.  Instead, Zelda and Impa are Link's connection with the royal family, so we see more of them than the king.  The king is too busy trying to save the kingdom to worry about a little kid.  But he probably did not last long.  Ganondorf attacked the castle.  That much is certain.  The dying guard in the market attests to that, along with Zelda running away.  Now, if you staged a successful coup, who would you kill first?  That's right, the king probably was killed.  Ganondorf may have wanted the Triforce more than anything else, but he wanted to be king as well.  "I am Ganondorf, and soon I will rule the world."  He's not going to let the king live. 
    
So the first king met his fate against Ganondorf.  Now what about the LttP king?  We actually see him, when you beat the game.  The odd thing is, he appears with the subtitle "The Return of the King."  What does this mean, besides the fact that Nintendo is a Tolkein fan?  Just where or from what is he returning from?  We know that his biggest fault, like the OoT king before him, is his distinct lack of character judgement.  He thought Agahnim was a good guy (granted, so did everyone else, so I'll excuse it).  Agahnim became a trusted advisor.  Now two different different scenarios can work here, but I think the second one is better.  First, the king may have fled for his life after Agahnim imprisoned Zelda and revealed his true nature.  Second, Agahnim may have cast some type of sleep spell on the unfortunate king.  The first one may fit the title "Return of the King" better, but it does not make sense.  Would a king run away from his responsibilities and his daughter?  Not really.  Sure, he could have been forced to flee by the altered guards, but some were still fine at the beginning of the game.  And besides, the instruction manual states that there are rumors that the king has been incapacitated somehow (I'll update this soon when I reread it), which supports the sleep spell theory.  Either way works, and we have no proof.  But he got off lucky either way.  Agahnim had no reason to kill him.  He was not trying to become the king; he was practically ruling the country anyway.  Thus, he did not have to die.
     
Now to our final king.  He probably died too, but it wasn't his fault.  He thought Ganon was dead.  But at least he was smart enough to protect the Triforce.  Somehow, Zelda managed to get Wisdom out of there, even though Ganon managed to get Power.  Once again, Ganon was aiming for leadership, so I doubt the king would have survived.  He was probably killed before Link even got his sword.  So obviously, there was no king in that game.  That would also explain why there was no king in AoL.  That and why Zelda (the one from LoZ), was not in the game.  She was Queen.  She did not have time to deal with Link and his birthmark.  She was too busy trying to rebuild after Ganon's destructive reign.  Rather simple. 
    
That just about wraps it up.  The kings are generally not importsnt to the plot of the games, so they just aren't shown.  That and the fact that they seem to not be able to live long enough.  So I hope that clears up everything.  Hopefully, soon, we will actually see a king in one of the games.  I'm not sure about Majora's Mask, but I believe there isn't any kingdom at all.  And I haven't a clue about the new Game Boy games.