I think there may be a case for some sort of special handling for riddles that are notable for some reason, such as appearing in a story. I'm thinking of things like the Sphinx's riddle in the Oedipus story or the riddle game in The Hobbit and the like. I've been tempted a couple of times to post some of the riddles in Jane Austen's works. I would suggest posting the riddle with a brief introduction saying why It's noteworthy, tagging it as "puzzle-history" and then following up with a community wiki answer.
If it doesn't qualify as "puzzle-history" but comes more under the heading of "crappy riddle that most people have already seen" then I'd be very tempted to close it like any other bad puzzle.
On the other hand, according to the tour this is supposed to be: "a library of detailed answers to every question about creating, solving, and studying puzzles." I don't believe that's what we are but it's what we say we are. If that is true, then I think it means that we should have and entry for "what's black and white and red all over" with a community wiki answer that explains what the accepted "correct" answer is and likely some discussion about why it's not an especially good riddle. If we do have this, I would suggest having some sort of a template saying that this ought to be preserved as a reference entry due to... whatever.
The problem is that this doesn't fit our model. "Black and white and red all over" is clearly too broad. It's also (in my opinion) a crappy riddle. Do you down vote it or not? Does a riddle (or any other puzzle) acquire some sort of worth after it has crossed some sort of notoriety threshold? How well known does a bad riddle have to be before it is worth preserving?