It was recently asked on the MO meta whether it was ok to post interesting bit of mathematics one had stumbled across on MO (http://tea.mathoverflow.net/discussion/1554/how-to-use-mo-as-a-multiplicator/).
The replies seem to generally be along the lines of "no, please don't do this, unless you really have a question you want answered".
Similarly, here on MSE, we occasionally have people asking if they can do this (since the FAQ says they can), and the consensus seems to be that this should at least be kept to a minimum.
On the MO meta, however, someone mentioned that it would be nice to have an SE-structured site for such things, ie a site where one can post interesting bits of mathematics one finds various places and which seem like they might also be interesting to other mathematicians (so ones that are probably not known to most mathematicians).
I have started this meta thread to ask if people think this will be doable (both in terms of getting such a site approved and in terms of moderating it).
One issue with moderation such a site is at what level one wants the mathematics, and how to make sure it does not get cluttered with a bunch of things that are well-known to anyone at some level.
Another concern would also be whether such a site is really suited for the Q&A format, as it is not clear what a good answer to such a bit of mathematics should be (maybe interesting applications of that bit of mathematics?).