1) he never had kids and it's not so strange considering his athletic past
2) he had kids, but they are all decent and well-behaved human beings, who didn't attract attention of the press with sick escapades
Well, I looked it up and now I am happy to inform you that Governor actually had FOUR children - all with the same woman, his wife Maria Shriver. Here you are - I even found a picture:
Nice looking family, I think. I actually like Mr. Schwarzenegger very much a honestly think than he is a really cool guy. Although I never in my life will manage to write his name correctly. It's OK, I'll copy-paste.