Some say that Jesus did not really die on the cross but that he just fainted. The recorded information in the bible makes it very clear that Jesus was dead.
The custom was in bible times that when a person was crucified their legs were sometimes broken to speed up the process of dying. Here is what happened with Jesus;
31Now it was the day of Preparation, and the next day was to be a special Sabbath. Because the Jews did not want the bodies left on the crosses during the Sabbath, they asked Pilate to have the legs broken and the bodies taken down. 32The soldiers therefore came and broke the legs of the first man who had been crucified with Jesus, and then those of the other. 33But when they came to Jesus and found that he was already dead, they did not break his legs.
John 19:31-33 (NIV)
The Roman soldiers recognised that Jesus was dead. They did another test too, just to make sure he was dead;
34Instead, one of the soldiers pierced Jesus’ side with a spear, bringing a sudden flow of blood and water. 35The man who saw it has given testimony, and his testimony is true. He knows that he tells the truth, and he testifies so that you also may believe.
John 19:34-35 (NIV)
The water and the blood being divided were also a sign to the Roman soldiers that Jesus was dead.
Dr. Stroud (On the Physiological Cause of the Death of Christ, London, 1847) basing his remarks on numerous postmortems, pronounced the opinion that here we had a proof of the death of Christ being due not to the effects of crucifixion but to “laceration or rupture of the heart” as a consequence of supreme mental agony and sorrow.
Jesus truly died on the cross.