As far as I know, they all worship the same God. The Prophets are generally sent down to guide people who have gone astray because if they hadn't gone astray, there would be no reason to send a Prophet.
Jesus was sent down to guide the people, but the Jews refused him. The Christians decided to follow the way of Jesus, following the right path to worship, except they then decided to give Jesus the status of being the son of God and also created the Trinity. This brought them far from the direction that God wanted for them, as can be seen when God sent:
Muhammad, the final Prophet to guide them back from the wrong path. The Christians were committing the most grieveous of sins: shirk (taking other Gods besides God), by raising up Jesus to a Godhood status and God did not appreciate this. He sent Muhammad to guide people in the correct way of worship, thus creating Islam. Muslims believe that Jesus was not the son of God, but was just a Prophet, like Muhammad and all the others who came before.
I can't recall any quotes from the Quran off hand regarding Judaism, but I know there are many times when the Quran speaks of God sending Jesus to the people, how the Christians made his Prophet to become his son, which angered God.
So in the perception of Islam, I believe they all worship the same God, but likely neither of the other two Religions would believe the same thing. If they did, then it would be easier to accept the two Prophets Jesus and Muhammad and there wouldn't be a split in the Religions. After all, if Christians believed that the Muslim God was also their Christian God, then they would need to accept the Prophet Muhammad as another of his Prophets and that the Quran is the word of God and if they did that then they probably would be Muslims and not Christians.