Everywhere you look you see speculations concerning Caroline Kennedy's interest in running for the U.S. Senate seat being vacated by Hillary Clinton. Less visible have been a couple of articles reporting trial balloons by former Florida Governor Jeb Bush concerning his running for a Senate seat. There is a name for this kind of thing: dynastic politics.
Dynastic politics isn't new in the United States. Second President John Adams' son John Quincy Adams was elected our sixth President. And Franklin Delano Roosevelt was a fifth cousin of Theodore Roosevelt. Maybe the most extreme example is the Udall family which, while containing no presidents, has spawned several senators and representatives in the mountain West. The Kennedys of Hyannisport are another current example.
However, just because we've done this before doesn't make it a good idea. I believe we are better off avoiding dynastic politics, the most extreme form of which is the inheritance of kingships in countries with royal families (the U.K., Sweden, Japan, the Netherlands, etc.). Now that most kingships are essentially figureheads, inherited royal leadership isn't a big problem. It certainly was a problem when kings were true CEOs and some real dopes inherited thrones.
Dynastic political families are more typical of third world countries than of first world true democracies, or should be. When the U.S. elects people to national office the roles are anything but symbolic.
The bottom line: Having a famous name is not a qualification for office.