Judaism barely spends any time discussing what may or may not happen when we die, in fact, there's barely any mention of this subject in the Tanach (Jewish Bible) at all.
There are some loose theories of what might happen though:
* When we die, our souls are cleansed of any wrongdoings. This is done by our accounting of every action done in life. It's believed that this process takes no longer than 12 months but most people don't do enough bad in life to warrant it taking a full 12 months.
* Our souls return to HaShem to wait for the world to come.
* Our souls may be reincarnated into different people so that we have additional chances to work to become closer to HaShem.
* Those souls that choose to be truly evil in life, cannot survive the process of cleansing and cease to exist.
The afterlife is detailed at length in the Talmud (unlike what the above comment says). A full 20 pages of Talmud (Sanhedrin 90-110) are given to this subject. The afterlife is also referred to briefly in Torah (Bible) verses such as Genesis 15:15, which states that "You (Abraham) will come to your fathers in peace and will be buried in good (ripe; full) old age". This does not mean merely to be buried with one's forefathers, since Abraham was not buried with them. Such verses are stated many times.
The prophets are more explicit with such references (such as Isaiah 26:19, Daniel 12:13).