What is the least expensive way to annihilate humanity?
While perfectly within the realm of worldbuilding, do we really want to answer these sorts of questions? Imagine if someone were to give a really, really good answer, and that some extremist group were to find inspiration in the answer.
That would not be fun. What do the people here think? Should we have a range of questions that are too close for comfort?
Although at one hand I have grown up in environment advocating freedom of information like the other two answers do, I do believe their arguments are intrinsically flawed, because they do not account for the responsibility one holds when being trusted with information.
Unlike in the past knowledge can nowadays equate power far easier than it used to. To just give a very down to the earth example to prove the point: passwords. Passwords are secret pieces of knowledge that through their obscurity provide a lot of security. If you have the knowledge about a certain password it gives you a lot of power. And thus, when given knowledge, one does have the responsibility to share it responsibly. Now, to give a more practical example of knowledge that unlocks power: Lets say the following question would be fully on topic:
What is the cheapest and easiest way one can create the most lethal bomb using publicly available materials?
and you're a chemist who is able to build an extremely lethal bomb using stuff anybody has at home. Should you share that publicly? Personally I would argue that that's incredibly irresponsible. Humans tend to act irrational from time to time against their nature (e.g. due to depressions) and the more power those humans have at their fingertips, the worse the consequences can be.
Does that mean we should suddenly ban lots of questions? I don't think so. Questions that will too easily give people unproportionally much power are definitely questions one should be mindful of (for example "What kind of human inflicted wounds are the most lethal?" can be easily wrapped in a nice 'I want to design a race of assassins' package, but is not an answer that I think a doctor should answer). A question how to annihilate humanity for cheap however doesn't really seem like something that we need to be wary of.
Hmm...
Censorship isn't really a good way to prevent bad things from happening, if anything having a good body of work on potential doomsday scenarios could lead to better preparation and prevention.
A while back Stack Overflow had a similar discussion on the ethics of answering "malicious" or "hacker" questions, it was determined that making these methods public knowledge could/would lead to better security. Basically a computer virus is only effective if your anti-virus software hasn't heard of it yet.
Similar arguments could easily be made here...
Inspiration comes from many, many sources. If you go looking for these things, you'll find hundreds. Most of the people who give answers here, probably read about them in a book in the first place. Many of the others are simply made up on the spot. In both cases; an extremist looking for them will find the same answer.
Even if there's the miracle case of someone having a flash of inspiration that no person has heard before, if it's that good it'll spread to both sides quickly and by posting it at least it's out in the open. Imagine if an extremist had the flash of inspiration and nobody had posted it openly before, then there'd be no preperation for it.
Besides; as they say: ideas are a dime a dozen. All of these answers are just pointers. With or without them, it takes a huge amount of effort and planning to actually do anything. Knowing that you can spread a biological agent through the water supply (seriously, how many B-movies have this plot, again?) is one thing, actually getting your hands on the biological agent and access to the water supply is a completely different affair.
Now, if people were starting to give real-world addresses on where you can buy said biological agents and names of people working at water treatment facilities... but that'd be illegal, so we don't need any extra rules against it.
After some thought, I'm of the opinion that questions (if on topic) are fine, but I personally won't post answers, if I think doing so might lead to harm. YMMV.
