In my case, people often comment about my children's looks. About 85% of the time I'm out with them, someone will stop me and say, "My god, your children are stunning. You should get them into modeling." or some variation of that. It's flattering (and of course, I think they're gorgeous), but I also don't want them to think that they're only a pretty face.

After 4 years of this, I've now started replying something along the lines of, "Yes, we're really lucky. They're also bright and well-behaved." or if I'm feeling cheeky, "They're so lucky. They got their father's looks and their mother's brains."

I would expect that you can deflect the intelligence comments with something like, "Well, everyone has to work hard to reach their full potential..."