TurboTax asks the question "Do you have children or financially support another person?". I have children but do not support them. Do I answer this question Yes or No?

If you do not support them answer No

I've also thought that this question was worded rather vaguely. An example of a better question might be.....

"Do you have children or another person that you financially support?".

No the wording is correct ... you could say yes if you have children.  It is possible that you can claim child related items even though you do not support them as long as the child is under the age of 19 and is not self supporting.  However if they are not your child then you MUST support them.  

What would simplify this would be if they were separate questions with yes/no radio buttons...

Do you have children ?

Do you support anyone else ?