I read that Jesus was charged with the allegation that he claimed to be the "King of Jews" . What are the evidences of this charge and other charges, if any, on Jesus? I am only interested in the charges leveled against him in the (Roman) court, and did he plead guilty?
There wasn't really one there were just a few supposed reasons. The certain Jews who wanted to see him executed claimed it was for blasphemy in making himself out to be God, or alternatively for supposing him to have violated the Sabbath.
Yet the rulers of the Jews only had derivative powers granted by the Romans and didn't have the authority to actually execute criminals, so they needed to pass this task along to the Romans, so they delivered him to Pilate under the accusation that as someone who has made himself out to be king, he is not loyal to Caesar.
Upon actually trying the case, Pilate admits that he found no fault in him, however ultimately Jesus' conviction was a matter of political expediency. The Jews were pressuring him and he was more interested in keeping the peace.
It's comparable to police shutting down a peaceful protest on the charge that they lack a noise permit but really because it upsets a favored politician.
For the civil trial, Luke's account gives the most detail about the charges, Luke 23:2 (NIV):
and Luke 23:5 (NIV):
The "subverting out nation" charge may be a religious charge, in which Pilate is, of course, not concerned except with how it interferes with ruling the region. The statement in Luke 23:5 seems to be the religious leaders pointing out that this is causing trouble about which the Romans should be concerned. Anyone that could draw crowds of thousands of people in relatively remote places would naturally be a concern for established authorities, especially given the Jewish history of rebellion (e.g., see Esther 3:8--even after the Babylonian scattering, they were recognized as being non-conformists--and Ezra 4:12-16, speaking of Jerusalem as historically a rebellious city).
The payment of taxes charge is clearly a false charge. Jesus' famous "render unto Caesar" statement (Matt. 22:21, Mark 12:17, Luke 20:25) makes that clear.
On the charge of being King of the Jews, Jesus states that this charge is effectively true (Matt. 27:11, Mark 15:2, Luke 23:3, John 18:37), but his statement recorded in John 18:36 points out that he is not a threat to Roman rule in the traditional political/military sense:
As Affable Geek points out, Pilate knew that Jesus was not guilty but chose political expediency over truth (after all, "What is truth?").
The charge against Jesus was that of blasphemy- according to the Pharisees, Jesus himself was claiming to be God.
Matthew 26 records the "trial" in the Jewish Court
Whether or not the charges are "true," of course, hinges on whether or not Jesus was God. His prophecy of destroying "this temple" (referring to his body, not necessarily the building) was destroyed, and resurrected after three days. If, in fact, he was God, then it isn't technically blasphemy - but it still seems as though Jesus' trial was supposed to be a setup from the beginning.
Matthew 27 picks up the Roman charge, but he is never convicted of that. As Matthew records it:
Here we have Pilate giving into the mob - nothing legal about it.