This was an interrogatory question in a civil lawsuit in federal court
If you have counsel, you should put this question to your counsel and let him or her guide you in deciding whether you have a good-faith objection that you can interpose to this discovery request.
Generally one must answer truthfully and fully all relevant discovery inquiries during pretrial proceedings, unless the response would reveal information that is privileged or unless the court has sustained an objection to the request -- e.g., an objection based on grounds that the request is really just intended as harassment and that it is not relevant.
The fact that you've been a party to other litigation is a matter of public record, and the details regarding that other litigation are almost certainly NOT privileged unless the inquiry is specifically directed to legal advice you privately sought or received in connection with it.
The definition of relevancy is "reasonably calculated to lead to the discovery of admissible evidence," which is a very flexible standard. If you're involved in commercial contract litigation or a personal injury case, then quite arguably your divorce or child custody records might not be relevant, and an inquiry into them might be intended only to harass, so your objection might be sustained.
But most judges -- including federal magistrates who typically rule on discovery disputes -- lean pretty strongly in favor of full disclosure, and they use a very broad notion of what is "reasonably calculated" to lead to admissible evidence. More often than not, an objection to a discovery request asking about other litigation is likely to be overruled. Perhaps worse, sometimes such objections are interpreted -- by one's opponents, and sometimes by the judge -- as suggesting an intention to cover up or hide one's past. You don't want to be making that impression.
This kind of judgment call -- as to what is and what isn't a "good faith objection" -- is exactly the kind of thing you most need counsel for. And if you make a misjudgment through ignorance or inexperience, the consequences could be very severe, possibly including sanctions in the form of fines, striking of claims or defenses, or even contempt of court. Tread cautiously, and whatever you do, don't just pretend the prior litigation didn't exist: Either disclose it, or else make a timely written objection to disclosing it.
The answer is "it depends." It depends on the relevancy of the other lawsuits. I will give you an example.
Let's say you are suing for personal injuries and you were a party to a simple divorce proceeding 15 years prior, or a breach of contract case years prior, or a real estate lawsuit years prior. Those probably have very little, if any, relevance to the current case. But if you had another personal injury suit 1 year prior, that one is probably relevant. So it depends.
But your attorney should timely object to the question if you were a party to a previous lawsuit that simply has no relevance to the current case. An interrogatory must be sufficiently limited in time and scope.
If you do not care about disclosing the information, you can disclose it subject to the objections.
Good luck to you.