These principles are the beliefs of observant Jews through-out the ages, and were summarized by Rabbi Moses ben Maimon (AKA Maimoniedes or Rambam).
1) I believe with complete (perfect) faith that the Creator, Blessed is His Name, creates and guides all creatures, and that He alone made, makes, and will make everything.
2) I believe with complete faith that the Creator, Blessed is His Name, is unique, and there is no uniqueness like His in any way, and that He alone is our G-d, Who was, Who is, and Who always will be.
3) I believe with complete faith that the Creator, Blessed is His Name is not physical and is not affected by physical phenomena, and that there is no comparison whatsoever to Him. (ie There is nothing what so ever to be compared to Him.)
4) I believe with complete faith that the Creator, Blessed is His Name, is the very first and the very last (G-d is eternal.)
5) I believe with complete faith that the Creator, Blessed is His Name--to Him alone is it proper to pray and it is not proper to pray to any other (Only G-d is to be worshiped and obeyed. There are no mediating powers able freely to grant man's petitions, and intermediaries must not be invoked.)
6) I believe with complete faith that the words of the prophects are true.
7) I believe with complete faith that the prophecy of Moses our teacher, peace be upon him, was true, and that he was the father of the prophets -- both those that preceded him and those who followed him. (Moses is unsurpassed by any other prophet.)
8) I believe with complete faith that the entire Torah now in our hands is the same one that was given to Moses, our teacher, peace be upon him.
9) I believe with complete faith that this Torah will not be exchanged nor will there be another Torah from the Creator, Blessed is His Name.
10) I believe with complete faith that the Creator, Blessed is His Name, knows all the deeds of human beings and their thoughts, as it is said, 'He fashions their hearts all together, He comprehends all their deeds' (Psalm 33:15)
11) I believe with complete faith that the Creator, Blessed is His Name, rewards with good those who observe His commandments, and punishes those who violate His commandments.
12) I believe with complete faith in the coming of the Messiah, and even though he may delay, nevertheless I anticipate every day that he will come. (of course, the Jewish view of the Messiah and the messianic era are not the same as those of the Christain faiths).
13) I believe with complete faith that there will be a resuscitation of the dead whenever the wish emanates from the Creator, Blessed is His Name and exalted is His mention, forever and for all eternity.
I was asked by a reader to clarify a couple of the articles of faith above. Not wanting to make it difficult to read the original statements, I am putting my clarification here.
12) The Jewish idea of a messiah is an anointed king. There have been many messiahs in Jewish history, many who bore the title annointed. For example, King Saul was refered to as "the L-RD's annointed". King David was likewise annointed by Samuel, and this a messiah. All of the priests, from Aaron on, are the annointed of the L-RD. They were all anointed for a specific post or job, be it king or priest. There is even one king, Cyrus of Persia, who is not of the children of Israel and yet was refered to as G-d's annointed. He was annointed for a specific task, to overthrow Babylon and allow the Jews to return to the land of Israel.
So, what about "the" messiah? Well, in the future, there will again be a king who is annointed over the children of Israel. This time is refered to as the messianic age. This king will be, like all the other kings of Judah, be of the Davidic line. That means his father must be a direct decendant in the male line, of King David and his son Solomon. His mother's mothers lineage doesn't determine if he is decendant of King David, so it doesn't matter if she is or is not. What matters is that his mother must be Jewish. Both, of course, are human, as only humans can claim decent from another human and thus pass on the lineage.
The Jewish messiah will be fully human. He will in no way be supernateral. The miracles of the day, be it the destruction of those who seek to destroy Israel, or the splitting of the mount of Olives, will not be done by the messiah, only by G-d (remember, the messiah is to be a human totally and utterly in the Jewish view).
Certain things must happen in the messianic age for it to be the messianic age. If they do not occur, we Jews know we are not dealing with the Jewish messiah nor has the messianic age arrived. Among those things are the ingathering of all the children of Israel, all the Jews, from the whole world. Peace must be occur after the attempted destruction of Israel, a peace where "nation shall not lift up sword against nation, neither shall they learn war anymore". The knowledge of Torah required by all (ie, the seven laws of Noach) will come forth from Jerusalem. "... In those days, ten men from nations of every tongue will take hold--they will take hold of every Jew by a corner of his cloak and say, 'Let us go with you, for we have heard that G-d is with you.'" (Zech. 8:23). The third Temple (the one invisioned by Ezekiel) will be built. If these have not happened, than a Jew says the messiah has not yet come. Thus it is that we still await our future Davidic king (lowercase k).
13) This is the belief in resurrection of the dead. A belief the Sadducees (read Roman collaborators) of the second Temple period did not hold. It means that in some way, those who have died will return to life in some way in the messianic era. One passage in the Tanach said to refer to ressurection is Isaiah 26:19 "Your dead shall live, my dead bodies shall arise -- awake and sing you who dwell in the earth! -- for your dew is as the dew of light, and the earth shall bring to life the shades."