That was then. But, now, some of the biggest brand names in politics are showing signs of growing stale.
In Connecticut, Sen. Chris Dodd -- himself the son of a long-serving senator -- was forced out of his re-election race by sagging poll numbers. In Nevada, the two Reids on the ballot -- Sen. Harry Reid, who's running for re-election, and son Rory, who is running for governor -- look like they're getting in each other's way.
"Right now, the insiders are on the outs," said John J. Pitney, a politics professor at California's Claremont McKenna College who focuses on Congress. "In an anti-incumbent climate, being the incumbent who's the son of an incumbent is probably not a good thing."
Prominent political families still dominate in Congress; from the Udall cousins in the Senate to House Speaker Nancy Pelosi (the daughter of a former House member), and from Rep. Mary Bono Mack (the widow of one former House member who's now married to another) to Rep. Rodney Frelinghuysen, the sixth Frelinghuysen to represent New Jersey in Congress.
Beau Biden stands a good chance of taking over his father's old Senate seat, in Delaware, should he choose to run.
Congressional races this year feature relative newcomers with familiar names including Rand Paul, the son of Rep. Ron Paul, R-Texas; Ethan Hastert, former House Speaker Dennis Hastert's son; and Paul Thurmond, the son of the late Sen. Strom Thurmond, R-S.C.
Yet the last election cycle saw both a Dole and a Sununu lose their re-election races. Former Rep. Joe Kennedy, D-Mass., ultimately joined his cousin Caroline Kennedy in choosing not to pursue Senate seats, after other family members suffered defeats in bids for higher office.
Perhaps nowhere are the complications of family ties more evident than in Nevada, where Senate Majority Leader Harry Reid stands as perhaps the most endangered Democratic senator in the nation.
Son Rory Reid rode the family name to become chairman of the Clark County Commission. But now that he's running for governor, dad's coattails look like a drag, with the elder Reid's cratering approval ratings affecting the younger Reid's prospects.
"This year, it's not that it's a mixed blessing; it's that we're going to find out how bad the family curse is," said Jon Ralston, a veteran Nevada political analyst. "The issue of the two Reids cuts against both of them. They're hurting each other."
One lesson of recent years: While a family name can get a candidate an early advantage and maybe even help win an initial race or two, it's no guarantee of long-term success.
"Over time, you've got to demonstrate an ability to serve the people who elect you," said former Sen. John E. Sununu, R-N.H. "Like any other politician, some succeed, and some fail."
Sununu's famous name -- his father was governor of New Hampshire and chief of staff to President George H.W. Bush -- gave him an early edge as he launched his political career. But it didn't save him from a Democratic sweep that ousted him from office in 2008.