UPDATE: Jeremy disagrees. He notes that all the examples I've given that don't have apostrophes are singular:
The analogies Ann draws doesn't work, because they are all instances of de-possessiving a potential possessive by making it singular--if we would say "individuals' rights", there should be an apostrophe, but if we talk about the same thing by saying "individual right", we essentially imbue it with a higher degree of abstraction--I'm sure there must be a fancy name for it--such that it's no longer a possessive. You write "human rights" but if you wanted to write "humans' rights", the possessive belongs. To take two common examples, some people refer to "children's rights" and "prisoners' rights", both of which should have possessives, while other people nowadays refer to the same thing as "child rights" and "prisoner rights."First, it should be "The analogies Ann draws don't work." And I'm just saying that because I want to be right about something.
Second, I'm going to exclude the example "human rights" because "human" is an adjective. "Human" is a noun and "humans" ought to be added to Jeremy's sidebar list of horrible words. They are clearly worse than "impact" as a verb! "Humans" is, at best, jocose. (Authority: Follett!) But I'll hedge on this opinion, because it seems open to the criticism that the rights are not human. They are the rights of the human being.
Third, "prisoners rights" just restates the problem whether the apostrophe is right or not: people hear the "s" and so they think about whether to add the apostrophe, and they may be making the wrong judgment.
Okay. "Children's rights" is the important example here, because we happen to have lucked into an irregular plural, so we know the "s" has to be there only as a possessive, and the apostrophe is required. What force prevented us from adopting the idiom "child rights"? In Jeremy's theory, it would have to be that for some reason we declined to perform the step of abstracting the notion of "the child," which is also what has happened with "states' rights." It might be the force of the irregular plural that kept it from declining into an abstract. But what prevented "states rights" from going singular, given that it's a pretty abstract thing? I think it may be the context of thinking about what belongs to the states as opposed to the national government. We always say things like, "This should be left to the states." It would be misunderstood if we changed that to "This should be left to the state," because "the state" is a generic term for government. Also "states rights" has a longstanding historical use: it's idiomatic. That does make me think that the apostrophe question might be resolved by referring to the historical texts: I do think that if you look at the pre-Civil War references to "states rights," you won't find the apostrophe. A more recent historical reference point is the "States' Rights Democrats" of the 1940s: I think they did use the apostrophe.
Anyway, I really want to the answer to be that the apostrophe does belong there, because I have a law review article with "States' Right" in the title ("Why Talking About 'States' Rights' Cannot Avoid the Need for Normative Federalism Analysis: A Response to Professors Baker and Young," 51 Duke L.J. 363 (2001)). I'm sure I've written the expression, with the apostrophe, many times in published articles. I'm also concerned that my argument for dropping the apostrophe is based largely on my assumption that the New York Times would get it right! That would be rather pathetic. And wait! I just did a LEXIS search of NYT articles written by Linda Greenhouse, who writes about the Supreme Court, and every one I saw had "states' rights" with the apostrophe. So all of this obeisance to the wisdom of the Times is in vain!
Vaguely related question I thought of while writing this update: Why don't we update the name of our country from United States of America to America's United States?