Did Martin Luther King, Jr. say
I mourn the loss of thousands of precious lives, but I will not rejoice in the death of one, not even an enemy
It's been going around the tweeterwebs today in response to Osama bin Laden's death.
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The source of that particular quote was a Facebook post by someone named Jessica Dovey:
@pennjillette I am the original author of the "MLK" quote. Somewhere my words got mixed with his. The post: http://i.imgur.com/cqtjw.jpg
Dovey said "I mourn the loss of thousands of precious lives, but I will not rejoice in the death of one, not even an enemy", and then quoted Martin Luther King Jr.:
"Returning hate for hate multiplies hate, adding deeper darkness to a night already devoid of stars. Darkness cannot drive out darkness: only light can do that. Hate cannot drive out hate: only love can do that." - Martin Luther King, Jr.
The Facebook post itself appeared as follows:
"There is within us a moral instinct which forbids us to rejoice at the death of even an enemy."
-- Henryk Sienkiewicz, Without Dogma (1891)
So, if Martin Luther King, Jr. did say it, he was likely paraphrasing Sienkiewicz (whether knowingly or unknowingly).
"The meaning of this story is not found in the drowning of the Egyptian soldiers, for no one should rejoice at the death or defeat of a human being. Rather, this story symbolizes the death of evil and of inhuman oppression and unjust exploitation." Martin Luther King Jr, Strength to Love, page 79
Proverbs 24, New International Version translation:
 Do not gloat when your enemy falls; when they stumble, do not let your heart rejoice,  or the Lord will see and disapprove and turn his wrath away from them.
This is similar to the attributed quotation. As a Protestant minister who championed a cause that placed himself and those around him in mortal danger, it is quite plausible that MLK saw fit to paraphrase and discuss this proverb and its application to life from time to time.
Similarly, the quotation "Darkness cannot drive out darkness" from the accepted answer can be considered a paraphrase of the Gospel of Mark, chapter 3:
 So Jesus called them over to him and began to speak to them in parables: "How can Satan drive out Satan?  If a kingdom is divided against itself, that kingdom cannot stand.  If a house is divided against itself, that house cannot stand...."
This pattern would also explain why other speakers and authors have similar quotations; perhaps they are paraphrasing the same passages, or even giving second-degree or third-degree attributions. (Some people attribute the "house divided against itself" proverb to Abraham Lincoln, for example.)