I've commented before on issues related to this, but I hadn't addressed this question directly because I think many have done so adequately throughout the blogosphere, and I didn't have anything special to offer beyond what was already being said. What I would have said was that there are many different questions involved in that question, and people might mean different things by it. Who did the actual deed? Who else was causally responsible for the deed? Who was morally responsible for the deed (which may involve different degrees or even levels of moral responsibility)? Most importantly, if you accept a divine purpose for it, then you have the question of who is the Aristotelian final cause of it (i.e. whose purposes were being fulfilled in it?).
Then Sunday, in the midst of a sermon on John 6:60-71, the head teaching elder of my congregation presented a simple biblical argument for exactly the sort of complicated picture that I thought would have had to trace out all the complex issues involved in all those questions. It's much easier than that. One expression occurs throughout the New Testament. Jesus was delivered up to be killed. It's worth looking at the specific statements about his being delivered up. Since the sermon was in a continuing series on John, the list begins there and eventually expands outward.
John 6:71 says that Judas was going to deliver him up. (Not every translation puts it that way, but that's the expression in the Greek, and the rest of the examples I give are also the same expression.) John 18:30 says that the high priestly leadership delivered him up. John 19:6 says that Pilate, against his own judgment, delivered him up (representing the Gentiles), which the gospels record alongside a fake ceremony of handwashing. Romans 4:25 says that our sins delivered him up (well, he was delivered up for our sins, but that amounts to the same thing when assigning responsibility). More strikingly, Romans 8:32 says that God delivered him up for us all. Finally, Galatians 2:20 has Paul describing the life he now lives by faith in the Son of God who "delivered himself up for me".
So who killed Jesus? The Bible teaches quite explictly that Judas of Iscariot, the Jewish leaders of the time (representing their people and the crowds calling for his death), Pilate (representing the chief Gentile authority of the time and the rule of Gentiles over Jews), every sinner, God the Father, and Jesus himself are all responsible (albeit in different ways). Those who deny that the Jews as a people are responsible for his death are denying the Christian scriptures, but that has to be taken in context with all the rest of this. It was part of God's plan, something Jesus himself willingly submitted to, because he wanted it to happen (as much as he dreaded it). As Mel Gibson realizes and expressed by having his hands do the nailing of Jim Caviezel to the cross in the film, every sinner is morally responsible for the killing of the Son of God.
This doesn't minimize the level of responsibility the Bible does assign to the Jewish people of the time (who had a communal sense of a people's responsibility for the moral failings of that people, as the prayers of Ezra and Daniel, in the ninth chapters of their respective books, reveal). Yet the perspective provided by the variety of ways the Bible talks of his being delivered up counterbalances any of that when it comes to how any Christian today should view Jewish people. Paul's heart crying out to his Jewish brethren in Romans 9 should make that obvious.