We all know that Steve Jobs will eventually leave Apple, and Apple's executive team has a responsibility to draft a succession plan to help minimize the turmoil when that day comes. To figure out what Apple might do, we can look to the past for other examples.
Ford Motor Company was founded in 1903 by Henry Ford. In 1918, at the age of 55, Henry handed the presidency of the company to his son Edsel. When Edsel died in 1943, Henry came back to Ford Motor Company ill, "mentally inconsistent, suspicious, and generally no longer fit" for the job.
Most of the board didn't want him to be president. Even with no official title, he'd been in de facto control of the company since Edsel took over. Nevertheless, the board elected him (rather than cross him), and he served until the end of the second World War. Gravely ill, he turned control of the company over to his grandson, Henry Ford II, in 1945. Henry Ford died two years later.
Steve Jobs has four children, the oldest of whom is Lisa Brennan-Jobs, a 30-year-old journalist. None have publicly expressed any desire to run Apple.