Are there any father/son, father/grandson, etc. winners of the Kentucky Derby or any other Triple Crown event?

Yes, there are a few- Gallant Fox, who won the Triple Crown and then sired Omaha, another Triple Crown winner. Gallant Fox also sired a horse named Flares, who was Omaha's brother and won the Ascot Gold Cup in England. Man'O War, who won the Preakness and Belmont as a 3 year old, went on to sire War Admiral, who was a TC winner as well- and he was Seabiscuit's grandsire. Reigh Count, who won the Derby decades ago, went on to sire Count Fleet, a TC winner, and then became the grandsire of Count Turf, who was another Derby winner. Another grandson of Reigh Count, named One Count, won the Belmont a few years later.

There are other examples- Alydar, who was the runner up to Affirmed in the TC races thirty years ago, was a prolific sire of stakes winners, including several Derby and Preakness winners. Alysheba was one example, as was Easy Goer.

Hope that answers your question.

Along with those already mentioned, Unbridled won the 1990 Kentucky Derby and sired 1996 Kentucky Derby winner Grindstone.

1957 Preakness winner Bold Ruler sired 1973 Triple Crown winner Secretariat and was a great grandsire of 1977 Triple Crown winner Seattle Slew.

1990 Preakness winner Summer Squall sired 1999 Derby/Preakness winner Charismatic.

Affirmed, the 1978 US Triple Crown winner sired Peteski, the 1993 Canadian Triple Crown winner. Peteski's damsire was Nureyev, and Nureyev is also Big Brown's damsire. Here's hoping Nureyev is the damsire of 2 Triple Crown winners.

It's very common actually. Stallions sire so many horses that it's kinda inevitable that their offspring will win big races too. AP Indy won the Belmont and Rags to Riches won it too so it's a father daughter sorta thing. Also, if you haven't seen Risen Star's 1988 Belmont runaway, you should watch it and compare with Secretariat's 1973. It's not as amazing as Secretariat, but it was really astoundingly close!

I would have to do research but I know that Secretariat and Seattle Slew both have had grandchildren who have won the Derby and or Belmont.

Rags to Riches has both Secretariat and Seattle slew in her pedigree. .