As a historian I know that while information (or in this case answers) are vital, but perhaps more important to good historical research are the sources consulted. Should we, as History.SE'rs, include referenced sources in our answers to add an air of legitimacy to both our answers and this site?
I know it's considered in bad form to answer your own question, meta or not, but I feel that it is appropriate here.
I think that sources should be listed to, as stated above, add legitimacy to our site as an academic resource but as well as to ensure that the information being posited as answers is in fact correct and not baseless interpretation.
I know this question might open up a can of worms regarding what source material is more "legitimate" than others, but I think that listing sources is a step in the right direction at the very least. (We can save the Wikipedia discussion for another meta question!)
I agree with GPierce. I browsed for few weeks now skeptics.SE. It deals also with alot history questions ("Did this really happen" and similar questions). Links/Quotes are prescribed for answers over there and it is imho a unique selling proposition vs. sites like reddit.
There are also pretty important and known effects in psychology concerning memory fallacies & deceptions (false memory syndrome) People have been interviewed and told wrong memories (unconscious lying). This happens esp. after decades (social memory and changing of history as it actually happened)
It really doesnt cost so much effort to find & include at least one link. I want to read facts here, no personal beliefs, no stories told by grandparents, opinions and interpretations, esp. for history of the 20th century.
What is dangerous about the long-term health of this site if we agree to not require sources is that people can feel free to post whatever they want as answers. This does not necessarily mean that these answers will be wrong, or not useful. But the purpose of ALL sites on Stack Exchange is to make the internet a better place, and to do so by providing useful information to those who seek it (among other things).
Undocumented answers are not necessarily the plague, but answers that lack utility are. When left to answer freely, users may feel it is acceptable to post answers that include opinion or subjective or superfluous material-- which is counter to everything that we're doing here.
Making people take the time to cite their answer and provide evidence may force them to do what many of us had to do when we first started using Stack Exchange sites (or Stack Overflow)-- learn how to to provide quality answers (and questions, for that matter).
For the record, I'm divided on whether or not History should require sources, because I agree with @Andrew Turvey's belief that this may scare people away. But as a historian, it makes me uncomfortable to provide or accept an answer without documentation to back it up.
I think it's very important to include sources, but I don't think there should be too much of a minimum bar. In general, I can look up sources fairly quickly to estimate the quality of an answer, and I think people will provide better answers if they are required to do minimal research to back them up.
When I discovered the site today I searched on "Northern Ireland" to see what it turned up. I went to one question and most of the answers don't include any sources, but the comments do in rebuttal. If people had actually done research they'd have easily turned up many useful titbits of information on this subject from Wikipedia. I guess the question is: how do you encourage people to focus on answers and not on comments?