In the Star Wars Original Trilogy, the only Jedi characters who die are Obi-Wan Kenobi and Yoda, who both disappear. This led many fans to believe that all Jedi disappeared when they died. However, the Expanded Universe and Prequel Trilogy have shown that this is not the case.
The Death of Qui-Gon Jinn
In Episode I: The Phantom Menace, Qui-Gon Jinn is the first Jedi character in the films who doesn't disappear when he dies, revealing that the disappearing act wasn't common among Jedi during that time. Despite the fact that his body did not disappear, however, Qui-Gon's spirit was able to live on in the Force after his death, returning to instruct Yoda and Obi-Wan after the destruction of the Jedi Order.
From Qui-Gon, Obi-Wan and Yoda learned how to become one with the Force at the moment of their deaths, making their bodies disappear and returning as Force ghosts. This skill had been lost to the Jedi for a long time, but would be passed down in the new Jedi Order founded by Luke Skywalker. Some Jedi could even manipulate their bodies after death. For example, Mara Jade allowed her body to remain corporeal, only disappearing at her funeral in an attempt to expose her murderer.
Those Who Vanish, and Those Who Do Not
Why don't all Jedi disappear when they die? Perhaps it's for practical reasons. The deaths of Obi-Wan and Yoda are important dramatic moments, and their bodies disappearing heighten the impact and symbolism of their passing. Anakin Skywalker also disappears when he dies, leaving his identity as Darth Vader behind literally (in the form of his suit and mechanical body parts) as well as symbolically. A great many Jedi die onscreen in the Star Wars Prequels, on the other hand, and it would be distractingly over-dramatic for all of them to disappear.
But the fact that Jedi bodies sometimes disappear and sometimes don't also helps demonstrate the changes in the Jedi characters. In the Original Trilogy, Yoda and Obi-Wan are meditative hermits -- no longer the warriors they were in the Prequels -- and the fact that their bodies disappear and become one with the Force reflects this change. Overall, we see that the ability to disappear at the moment of death and live on in the Force is not something typical and mundane, but is only possible for Jedi strong in the Force.