In Julius Caesar, why does Caesar say "Even you, Brutus?" before his death?
He doesn't, actually. He says "and you, Brutus?", sometimes read as meaning "even you, Brutus?", or perhaps "and you, as well, Brutus?". And he says it in Latin. The one moment in this Roman play where Shakespeare has someone speak in Latin. It's as if this colossal moment in the play: the central thirty seconds of action which define a whole world and the whole evening's entertainment - take on a wider historical significance by becoming "real". The Romans really do speak in Latin, for one line only.
Why does Caesar say "and you, Brutus?" though? Well, Thomas North, whose translation of Plutarch Shakespeare took the play from (largely) might help us here:
Men reporte also, that Caesar did still defende him selfe against the rest, running everie waye with his bodie: but when he sawe Brutus with his sworde drawen in his hande, then he pulled his gowne over his heade, and made no more resistaunce...
Caesar gives up when Brutus strikes (after "et tu...", in Shakespeare, he says "then fall Caesar"). Why does he give up the struggle, and accept his death? That is the question.
Is it because he knows he is already dying? Is he disgusted with Brutus? Does he believe that, if Brutus (noblest of the noblest, we are told) is involved, he deserves to be murdered? Is he heartbroken (as Antony later argues) that Brutus, "Caesar's angel", has conspired against him?
It could be all of them or any of them. That one's up to how you interpret the play.
Caesar obviously feels betrayed by Brutus. Looking into the actual history, Caesar did a lot for Brutus. When Caesar and Pompey were fighting for control of Rome, Brutus (and Cassius) sided with Pompey, leaving Rome with him and publicly declaring their allegiance to him. When Pompey was defeated, Brutus returned to the city. Caesar pardoned him and gave him a seat in the Senate (which greatly angered many, including Antony, who had remained loyal to Caesar). Now, this was more than likely a political move on Caesar's part--the people loved Brutus, as Cassius tells us in the play, and perhaps, a favor to Brutus' mother (it was rumored that Caesar had an on-going affair with Brutus' mother, Servillia, Brutus, as it is sometimes said, was NOT Caesar's son; Caesar's affair with his mother came after Caesar's rise to power in the army and politics).
So, after doing all of this for Brutus (when Caesar could have just as easily had him killed), Caesar, though portrayed as hard, insensitive and stoic, felt the ultimate betrayal. "And you, Brutus?--even you, after all I've done for you, still are going to be a part of this?"
I sometimes like to think it was Caesar's revenge on Brutus. Those are Caesar's dying words, and if Brutus is as sensitive and introspective as he is presented, those words probably haunted him and made him feel guilty until his death.