There are some foundational religious belief differences, of course. This is not the main reason Jews and Christians have fought for so long. The Christians have historically been intolerant of Jews as an ethnicity as well as a religion.
Among other differences, Jews and Christians also have different holidays. For instance, because Christians believe that Jesus is the son of God and was born around the end of our calendar's December, Christmas is celebrated. In contrast, the Jewish tradition of Hannukah takes place over 8 days and nights and commemorates Israelite victory in battle.
There are select members of the Jewish community who have labeled themselves "Jews for Jesus," meaning that they adhere to the traditions and standards of the Jewish faith (eating Kosher foods, etc.), but also believe that Jesus was, in fact, the Messiah or Savior that was prophesied in the Old Testament.
Both Jewish and Christian faiths are monotheistic, although basic, non-denominational Christianity defines the single God through the "trinity:" Father (God), Son (Jesus), and the Holy Spirit (the "voice" or "movement" of God Himself; commonly thought to be connected with the human conscience). Some scholars have asserted that Christianity is polytheistic because of this clarification of God's nature.
Christians are typically not bound by the Kosher diet like most professing Jews are (unless they make that personal decision on their own), and there are differences in the methodology of each group's style of worship, as well. You may wish to seek out an objective historical reference for this discussion post. Hope these few brief details help.
The main and most important difference in beliefs among Jews and Christians lie in the existance and belief in Jesus. Christians believe that Jesus was the Messiah (therefore why the New Testament is included in the Bible). The main reading, which outlines the system of beliefs in Jewish law is known as the Torah, and is very similar to the Old Testament of the Bible. However, the Jewish faith does not acknowledge Jesus as the Messiah, in fact they believe that the Messiah has not yet come. This also explains why the Christian World is on the year 2009 while the Jewish calendar is somewhere in the neighborhood of the year 6000 (the calendar did not restart when Jesus was born therefore there is no existance of B.C. or A.D.)
This is a huge and sensitive question and one that is hard to answer in a quick post. The 'correct' answer would cover a huge amount of history, religion, culture, politics, biology and philosophy.
But, in a nutshell, The Israelites were a tribe in ancient times. They believed they were 'the chosen people' and that their God gave them a 'promised' land called 'The Holy Land'. Their mono-theistic religion was a powerful new religious idea. The history of the Jewish people is recorded (with varying accuracy) in the Old Testament.
Then 2000 years ago, one Jewish man called Jesus claimed he was 'the son of God' and that he had many new religious instructions and changes.
Jews are people who believe the Jewish religion but don't believe Jesus.
Christians are people who believe the Jewish religion and Jesus.
and, by the way, Muslims are people who believe the Jewish religion, Jesus and Mohammed.