Only two. But yes, they are the only father-son championship winners.
Other fathers and sons who have both won Grand Prix are:
Gilles and Jacques Villeneuve both won Grand Prix, but only Jacques won a championship.
Keke and Nico Rosberg similarly both won Grand Prix, but in this case only the father has won a championship. So far.
Alberto Ascari and his father Antonio both won Grand Prix, though Antonio was killed before the F1 championship got underway. Alberto won two championships, and 13 races. Both were killed in action at age 36.
Nelson and Nelson Piquet jr. are a different story. The father won three championships, but the son hasn't had the same success. I suppose we could count Singapore 2008 as a half-win for him, though.
Less successful were the fathers, or sons, of the following families:
Mario and Michael Andretti. Mario won the title in 1978, but his son Michael only managed 13 races with McLaren in 1993. Much drama ensued.
Hans Stuck was a big name in the 1930s, and drove a handful of F1 races in the 1950s. His son Hans-Joachim managed 74 starts in the 1970s, and reached the podium twice.
Jack Brabham won three championships, but his sons Gary (2 attempts, 0 starts) and David (24 starts) never came close to matching his record in F1.
Satoru and Kazuki Nakajima never achieved much success in F1.
The same can be said for Manfred and Markus Winkelhock, but at least Markus can claim to have led a race. His only race: Nürburgring 2007.
For more details, check out this ESPN Article.
Edited by Nonesuch, 17 March 2014 - 08:15.