Traditional Judaism firmly believes that death is not the end of human existence. However, because Judaism is primarily focused on life here and now rather than on the afterlife, Judaism does not have much dogma about the afterlife, and leaves a great deal of room for personal opinion. It is possible for an Orthodox Jew to believe that the souls of the righteous dead go to a place similar to the Christian heaven, or that they are reincarnated through many lifetimes, or that they simply wait until the coming of the messiah, when they will be resurrected. Likewise, Orthodox Jews can believe that the souls of the wicked are tormented by demons of their own creation, or that wicked souls are simply destroyed at death, ceasing to exist.
Some scholars claim that belief in the afterlife is a teaching that developed late in Jewish history. It is true that the Torah emphasizes immediate, concrete, physical rewards and punishments rather than abstract future ones. See, for example, Lev. 26:3-9 and Deut. 11:13-15. However, there is clear evidence in the Torah of belief in existence after death. The Torah indicates in several places that the righteous will be reunited with their loved ones after death, while the wicked will be excluded from this reunion.
The Torah speaks of several noteworthy people being "gathered to their people." See, for example, Gen. 25:8 (Abraham), 25:17 (Ishmael), 35:29 (Isaac), 49:33 (Jacob), Deut. 32:50 (Moses and Aaron) II Kings 22:20 (King Josiah). This gathering is described as a separate event from the physical death of the body or the burial.
Certain sins are punished by the sinner being "cut off from his people." See, for example, Gen. 17:14 and Ex. 31:14. This punishment is referred to as kareit (kah-REHYT) (literally, "cutting off," but usually translated as "spiritual excision"), and it means that the soul loses its portion in the World to Come.
Later portions of the Tanakh speak more clearly of life after death and the World to Come. See Dan. 12:2, Neh. 9:5.
Belief in the eventual resurrection of the dead is a fundamental belief of traditional Judaism. It was a belief that distinguished the Pharisees (intellectual ancestors of Rabbinical Judaism) from the Sadducees. The Sadducees rejected the concept, because it is not explicitly mentioned in the Torah. The Pharisees found the concept implied in certain verses.
Belief in resurrection of the dead is one of Rambam's 13 Principles of Faith. The second blessing of the Shemoneh Esrei prayer, which is recited three times daily, contains several references to resurrection. (Note: the Reform movement, which apparently rejects this belief, has rewritten the second blessing accordingly).
The resurrection of the dead will occur in the messianic age, a time referred to in Hebrew as the Olam Ha-Ba, the World to Come, but that term is also used to refer to the spiritual afterlife. When the messiah comes to initiate the perfect world of peace and prosperity, the righteous dead will be brought back to life and given the opportunity to experience the perfected world that their righteousness helped to create. The wicked dead will not be resurrected.
There are some mystical schools of thought that believe resurrection is not a one-time event, but is an ongoing process. The souls of the righteous are reborn in to continue the ongoing process of tikkun olam, mending of the world. Some sources indicate that reincarnation is a routine process, while others indicate that it only occurs in unusual circumstances, where the soul left unfinished business behind. Belief in reincarnation is also one way to explain the traditional Jewish belief that every Jewish soul in history was present at Sinai and agreed to the covenant with G-d. (Another explanation: that the soul exists before the body, and these unborn souls were present in some form at Sinai). Belief in reincarnation is commonly held by many Chasidic sects, as well as some other mystically-inclined Jews.
The spiritual afterlife is referred to in Hebrew as Olam Ha-Ba (oh-LAHM hah-BAH), the World to Come, although this term is also used to refer to the messianic age. The Olam Ha-Ba is another, higher state of being.
In the Mishnah, one rabbi says, "This world is like a lobby before the Olam Ha-Ba. Prepare yourself in the lobby so that you may enter the banquet hall." Similarly, the Talmud says, "This world is like the eve of Shabbat, and the Olam Ha-Ba is like Shabbat. He who prepares on the eve of Shabbat will have food to eat on Shabbat." We prepare ourselves for the Olam Ha-Ba through Torah study and good deeds.
The Talmud states that all Israel has a share in the Olam Ha-Ba. However, not all "shares" are equal. A particularly righteous person will have a greater share in the Olam Ha-Ba than the average person. In addition, a person can lose his share through wicked actions. There are many statements in the Talmud that a particular mitzvah will guarantee a person a place in the Olam Ha-Ba, or that a particular sin will lose a person's share in the Olam Ha-Ba, but these are generally regarded as hyperbole, excessive expressions of approval or disapproval.
Some people look at these teachings and deduce that Jews try to "earn our way into Heaven" by performing the mitzvot. This is a gross mischaracterization of our religion. It is important to remember that unlike some religions, Judaism is not focused on the question of how to get into heaven. Judaism is focused on life and how to live it. Non-Jews frequently ask me, "do you really think you're going to go to Hell if you don't do such-and-such?" It always catches me a bit off balance, because the question of where I am going after death simply doesn't enter into the equation when I think about the mitzvot. We perform the mitzvot because it is our privilege and our sacred obligation to do so. We perform them out of a sense of love and duty, not out of a desire to get something in return. In fact, one of the first bits of ethical advice in Pirkei Avot (a book of the Mishnah) is: "Be not like servants who serve their master for the sake of receiving a reward; instead, be like servants who serve their master not for the sake of receiving a reward, and let the awe of Heaven [meaning G-d, not the afterlife] be upon you."
Nevertheless, we definitely believe that your place in the Olam Ha-Ba is determined by a merit system based on your actions, not by who you are or what religion you profess. In addition, we definitely believe that humanity is capable of being considered righteous in G-d's eyes, or at least good enough to merit paradise after a suitable period of purification.
Do non-Jews have a place in Olam Ha-Ba? Although there are a few statements to the contrary in the Talmud, the predominant view of Judaism is that the righteous of all nations have a share in the Olam Ha-Ba. Statements to the contrary were not based on the notion that membership in Judaism was required to get into Olam Ha-Ba, but were grounded in the observation that non-Jews were not righteous people. If you consider the behavior of the surrounding peoples at the time that the Talmud was written, you can understand the rabbis' attitudes. By the time of Rambam, the belief was firmly entrenched that the righteous of all nations have a share in the Olam Ha-Ba.
The place of spiritual reward for the righteous is often referred to in Hebrew as Gan Eden (GAHN ehy-DEHN) (the Garden of Eden). This is not the same place where Adam and Eve were; it is a place of spiritual perfection. Specific descriptions of it vary widely from one source to another. One source says that the peace that one feels when one experiences Shabbat properly is merely one-sixtieth of the pleasure of the afterlife. Other sources compare the bliss of the afterlife to the joy of sex or the warmth of a sunny day. Ultimately, though, the living can no more understand the nature of this place than the blind can understand color.
Only the very righteous go directly to Gan Eden. The average person descends to a place of punishment and/or purification, generally referred to as Gehinnom (guh-hee-NOHM) (in Yiddish, Gehenna), but sometimes as She'ol or by other names. According to one mystical view, every sin we commit creates an angel of destruction (a demon), and after we die we are punished by the very demons that we created. Some views see Gehinnom as one of severe punishment, a bit like the Christian Hell of fire and brimstone. Other sources merely see it as a time when we can see the actions of our lives objectively, see the harm that we have done and the opportunities we missed, and experience remorse for our actions. The period of time in Gehinnom does not exceed 12 months, and then ascends to take his place on Olam Ha-Ba.
Only the utterly wicked do not ascend at the end of this period; their souls are punished for the entire 12 months. Sources differ on what happens at the end of those 12 months: some say that the wicked soul is utterly destroyed and ceases to exist while others say that the soul continues to exist in a state of consciousness of remorse.
Adin Steinsaltz's The Thirteen Petalled Rose (Hardcover) (Paperback) (Kindle) is a complete mystical cosmology written by one of the greatest Jewish scholars alive today. It discusses the various levels of existence, the angels and demons that are created by our actions, the concept of reincarnation, and many other subjects of interest.
For an outline of Jewish thought on the afterlife, see Neil Gillman's The Death of Death : Resurrection and Immortality in Jewish Thought (Hardcover) (Kindle) . Gillman is a Conservative rabbi and a professor of Jewish philosophy at the Jewish Theological Seminary (a most important school for Conservative rabbis).
For information about the wide variety of Jewish views on what happens after death, see Simcha Paull Raphael's book, Jewish Views of the Afterlife. (Hardcover) (Paperback) Raphael, a Reconstructionist rabbi, takes a historical approach to life-after-death theories, exploring the views that predominated in each era of Jewish history.