Jewish sources don't deal extensively with the question of an afterlife, but Jews believe that in some form a soul lives on.
Some have argued that it lives on in repeated incarnations (gilgul neshamot
--which means the circle, or cycle, of souls). But most have contended that there is another world--Olam Haba,
the World to Come--where souls dwell in peace with their Maker.
In the words of Rav, a Talmudic sage: "The world to come is not at all like this world. In the world to come, there is no eating, no drinking, no procreation, no commerce, no envy, no hatred, no rivalry; the righteous sit with crowns on their heads and enjoy the radiance of the Divine Presence."
There are sources in Judaism that contradict this, seeming instead to argue that death is an end. Arguing for life, the Psalmist sings to God, "The dead do not praise you" (Psalm 115:17). And in the Talmud, one opinion is that talking about one who is dead is like talking about a stone--that is, the dead cannot hear us (Berachot 19a).
But it is only in modern times that Jews have largely lost faith in life after death. Throughout most of the Middle Ages, a jumble of beliefs in the afterlife prevailed: The World to Come, the advent of the Messiah, the reward and punishment of people after death.
Today, immortality is often recast. Some people argue that immortality is having one's influence endure. Being remembered is itself all the immortality we can hope for in this world. Still for others, memory is a less satisfactory result than immortality in its purest form. As Woody Allen once wrote: "I do not want to achieve immortality through my work. I want to achieve it through not dying."