Sibling Rivalry... When Will It End?

I'm sure any mother of more than one child will admit that THE hardest part of raising a family is making the children of the house get along with each other.  Lately I feel like they are all vying for my attention, fighting incessantly, and hurting each other more than ever.
 
"Share!"
"Don't take that from her!"
"You may not lay on your sister!"
"Yes, you can have one too!"
"No, he's not hurting you."
"I said share dammit!"
"Give that back!"
"Don't pull her hair!"
"It'll be your turn in a minute!"
"Share!"
"In a minute!"
"In a godforsaken minute!!!"

That's pretty much what my house sounds like every afternoon.  If I say nothing else all day, I say each and every one of those phrases at least 10 times in any given day.  Getting my children to get along is proving to be more and more difficult as they get older.  The girls are approaching 3 years old, and are not as passive and easily distracted as they once were.  Joey is getting older, wiser, and more manipulative by the minute, and has in turn become the World's Worst Sharer.  Sometimes I feel like I'm living in a war zone, just ducking to avoid a plastic domino to the head.

If I buy 2 of something, I should have bought 3.  If I buy 3 different items, I should have bought 3 of the same.  If we do happen to own a singleton toy of something, it more than likely is owned by Joey, and it more than likely NEVER gets played with because it's hidden somewhere so that "his sisters can't get it."  What good is that???  I've tried to explain to him that it doesn't even make sense, but more often than not his bed will be strewn with a series of favorite toys that no one (not even he) plays with.

So how do I stop the madness?  How do I teach my children to chill the you-know-what out and let each other play with whatever he/she/it pleases?  What works in your house?  The timer method?  The "if she can't play with it, no one can play with it" method?  Maybe I'm just destined to a life of referee-ing children that have lost the ability to share.  Or perhaps it's time I just sit back and let them battle it out, and the last one standing gets all the toys... (sounds kinda sick but fun, doesn't it?)