Was Jesus the Jewish Messiah?

The following is the most even handed summary of the arguments, although it is far from complete. I highly recommend not making a judgment based solely on the content of this post, but also read the material on the 8 links at the bottom of this post under the section "Sources and Further Reading". The following material is quoted from here.

The title "Christ," which was applied almost interchangeably with the name "Jesus" by Christians from the New Testament era onwards, comes from the Greek for "Messiah."

The Messiah is a Jewish hero-figure predicted by the Hebrew prophets to save the Jews and bring justice to the world.

Christians believe Jesus was and is this Messiah; Jews believe he is not and still await a future messiah. Presented below are basic outlines of the reasons given for both views.

Reasons for Jesus as Messiah (Christian Perspective)

Christian Argument	Jewish Counter-Argument
Jesus was born of a virgin. Matthew 1:22-23 fulfills Isaiah 7:14.	"Nowhere does the Bible predict that the Messiah will be born to a virgin. In fact, virgins never give birth anywhere in the Bible. This idea is to be found only in pagan mythology. To the Jewish mind, the very idea that G-d would plant a seed in a woman is unnecessary and unnatural." (5, p.31) "The Hebrew term in Isaiah “almah” which means a “young woman” is mistranslated as “virgin.” Honest Christian scholars now acknowledge that this is “a pious fraud” and now (see the new Protestant “Revised Standard Version” of the Bible) translate the word correctly." (5, p.33)
Jesus was born in Bethlehem. Matthew 2:4-6 fulfills Micah 5:2.	Jesus was likely born in Nazareth - the Bethlehem story has no historical foundation.
Jesus was from the line of David. Luke 3 fulfills Jeremiah 23:5, 33:17; Ezekiel 34:23-24; II Sam. 7:14; I Chr. 17:11-14, 22:9-10, 28:4-6.	A tribal line cannot be passed on through adoption, so Jesus cannot be "son of David" through Joseph. A tribal line also does not pass through the mother, and even if it did, Mary was not descended of David through Solomon. (6, p.2)
Jesus' side was pierced on the cross. John 19:33-37 fulfills Zechariah 12:10.
Jesus was the Suffering Servant. John 12:37-38; Acts 8:30-35; 1 Peter 2:21-25 fulfill Isaiah 52-53.	Isaiah 52-53 is referring to the people of Israel, not to the Messiah.
Jesus was God. John 8:58 fulfills Isaiah 9:6.	"Nowhere does our Bible say that the Messiah would be a god or G-d-like. The very idea that G-d would take on human form is repulsive to Jews because it contradicts our concept of G-d as being above and beyond the limitations of the human body and situation. Jews believe that G-d alone is to be worshiped, not a being who is His creation, be he angel, saint, or even the Messiah himself." (5, p. 31)

Reasons against Jesus as Messiah (Jewish Perspective)

Jewish Argument	Christian Counter-Argument
The true Messiah is to rebuild the Temple in Jerusalem—but Jesus lived while the Temple was still standing. Jeremiah 33:18	Jesus will do this at the Second Coming.
The Messiah will reestablish Jewish religious law as the law of the land. Jeremiah 33:15	Jesus will do this at the Second Coming.
The Messiah will save Israel." In the case of Jesus, the very opposite took place. Not long after his death, the Holy Temple in Jerusalem was destroyed, Jerusalem was laid to waste, and the Jews went into exile to begin a 1900 year long night of persecution, — largely at the hands of the followers of this self-styled Messiah!" (6)	Jesus will do this at the Second Coming.
He will establish a government in Israel that will be the center of all world government, both for Jews and gentiles (Isaiah 2:2-4; 11:10; 42:1).	Jesus will do this at the Second Coming.
The Messiah will return all exiles to their homeland. Isaiah 11:11-12 Jeremiah 23:8; 30:3 Hosea 3:4-5	Jesus will do this at the Second Coming.

Jewish response: The claim that Jesus will fulfill the Messianic prophesies when he returns does not give him any credibility for his "first" coming. The Bible never speaks about the Messiah returning after an initial appearance. The "second coming" theory is a desperate attempt to explain away Jesus’ failure. The Biblical passages which Christians are forced to regard as second coming don’t speak of someone returning, they have a "first coming" perspective. (6, p1)

Sources and Further Reading

1. "How do we know that Jesus is the Messiah?" ChristianAnswers.net.
2. "What proof do you have that Jesus was the Messiah?" Jews for Jesus.
3. "Evidence that Jesus Christ is the Messiah." Matthew McGee.
4. "Is Jesus Both Messiah and God?" Josh McDowell, A Ready Defense, ch. 22, published online.
5. The Real Messiah? A Jewish Response to Missionaries. PDF e-book published by Jews for Judaism.
6. The Jewish Messiah. PDF brochure published by Jews for Judaism.
7. Messiah Revealed.
8. "Mosiach: The Messiah." Judaism 101.