[FalconP]

Kirsty MacColl (who saidly had died in a skating accident), daughter of Ewan MacColl

Eliza Carthy, daughter of Martin Carthy -- Eliza is not exactly as famous as her father but she is definitely an up-and-rising name in British folk music.

 

[stuartr]

Ahh, nobody beat me to it:
Dmitri and Maxim Shostakovich: Composer/pianist Father, Conductor Son
David and Igor Oistrakh: Violinist Father and Son

The Strausses

I think Mary Chapin Carpenter's dad was famous too...famous being relative...she went to my high-school, which is the only reason I have heard of her, but I guess she is somewhat well-known.

 

[Megaptera]

The Wainwrights (Loudon Wainwright III/Katie McGarrigle and Rufus) come to mind. So do the Thompsons (Richard/Linda and Teddy).

Actually, as I think about it, I think Teddy Thompson may have played on one of Rufus Wainwright's albums.