Carrie Fisher is the only entertainment celebrity I can think of who is the child of 2 entertainment celebrities.
Oh, wait, Liza Minnelli comes close. I think of Vincente Minnelli as a celebrity, since a lot of the public in his time probably knew his name. (Some might disagree.)
Candace Bergen comes close, too, but her mom was never any mean shakes in acting (but she sure looked good in clothes!)
Might be pushing the definition of "Celebrity" (but then, so do others on this thread already), but how about Joseph Williams? Actually he would go even further - quintuple-distilled, if you like - since Barbara Ruick's parents were also famous in their time.
And for the Brits and Bond fans, a couple of relatives of mine - Rory Kinnear, son of Carmel Cryan (one of those faces you just know from somewhere, look her up - she's done quite a bit) and Roy Kinnear.
Don't know if she's been mentioned yet, but isn't actress/singer Charlotte Gainsbourg the daughter of model/actress Jane Birkin and singer Serge Gainsbourg?