NDAs are usually used in work situations to prevent employees from disclosing sensitive information. However, they cannot be used to prevent somebody disclosing a crime or harassment, discrimination etc. Yes, they are legally binding.
So, for example, if a celebrity (or anyone) hires a full-time nanny to look after their children then they may require the nanny to sign an NDA. The NDA would prevent the nanny from telling the world about what the celebrity got up to. That is, unless they were breaking the law or something in which case the NDA doesn't apply.
There is also something called 'misuse of private information'. This actually came up in the DW judgment. As part of the reasoning for why the judge decided not to uphold the injunction was that:
[234] "The Claimant has not pleaded misuse of private information, breach of confidence..."
If you disclose information (or threaten to disclose) about a person where they have a reasonable expectation of privacy about that information then they can apply for an injunction to stop you doing that or apply for damages.
Not all information about a person would be covered by this but it can be quite wide ranging at times.
For example, it can include taking photos of their children. Both JK Rowling and the singer Paul Weller were successful in claiming damages against organisations that published photos of their children.
If there is a reasonable expectation of privacy then, like in the DW case, the judge will then have to balance the human rights Article 8 (privacy and family life) against Article 10 (freedom of expression) to decide whether to grant an injunction or damages.