I would not mention anything about family on the CV as that can be a legal liability (in the United States, not sure about other countries) and prevent you from being interviewed.
The United States government specifically mentions that employers should NOT ask anything about marital or family status before a candidate is hired.
It is clearly discriminatory to ask such questions only of women and not men (or vice-versa). Even if asked of both men and women, such questions may be seen as evidence of intent to discriminate against, for example, women with children.
Generally, employers should not use non job-related questions involving marital status, number and/or ages of children or dependents, or names of spouses or children of the applicant. Such inquiries may be asked after an employment offer has been made and accepted if needed for insurance or other legitimate business purposes.
There is nothing in the law which prevents candidates from mentioning marital status on their own. With that said, it has been my experience that employers (and HR departments) will generally shy away from candidates who bring up their membership in a protected class as the risks of a lawsuit against the company for hiring (or not hiring) the candidate outweigh the benefits. There is much less risk in simply tossing the CV into the trash and not moving the candidate forward in the hiring process.
Why is this such a big deal?
For those unfamiliar with the legal system in the United States and why a company would want to avoid a discrimination lawsuit
- They are very expensive, take a long time to resolve, hurt internal morale, and generate bad publicity.
- Much of the damage to the company is done well before the case is over. Losing the case increases the costs, but winning the case does not fully repair the bad publicity or refund the lost productivity due to poor morale.
- Settling the lawsuit out of court, while not cheap, is usually less risky and less expensive than going to trial and potentially losing.
- Even defending against a frivolous case has a non-trivial cost
This article about why and how employers avoid employment discrimination has more information.
Because of the risk for potential damage, company policies and HR will try to limit even the slightest appearance of discrimination that might lead to a lawsuit. This includes prohibiting certain questions in interviews.
As pointed out by Steve Jessop, tossing out all CVs which mention a protected class is a form of discrimination, and will probably not be specifically mentioned in a policy. With that said, there are many other safe reasons to use for rejecting candidates at the resume stage, such as having too few or too many years of experience with the skills listed in the job posting. These types of reasons are more difficult to justify after a phone screen or in person interview, where the candidate could argue that the company decided to drop them because they sounded/looked like a particular gender or ethnicity.