When is it approriate to flag a post as spam? Today I hit the 5 flag limit because of 2 posts on RH, an inductive proof of Goldbach and some other junk. Each of these have aporox -5 votes or more. In general I have flagged as spam things of this sort or undergrad HW where the poster says it is homework. Besides putting a -1 vote does flagging as spam do anything? My hope is that the moderators delete spam but maybe it isn't so.

In addition to what Andy said, there is also a reputation penalty of 50 or 100 points for OP if something gets deleted via spam flags. (Irrelevant for new users, but documenting it is a severe measure.)

Thus, if you want moderators to have a look, I suggest to flag for 'moderator attention'.

My point of view here is that essentially no post made in good faith should be flagged as 'spam'; of course it can and should (if apppropriate) by closed and downvoted (and perhaps eventually be deleted). I see the latter measures as the standard moderation tools. By contrast 'spam' or 'offensive' flags are non-standard tools, only to be used in extreme cases that have a sense of urgency to them. A homework question is rather not in this category (except if somebody should continue to post such questions after being told not to do so). [I did not see the RH and Goldbach post, there it is harder to tell; might be or might not be.]

There is also a practical aspect to this. As far as I know if something gets deleted it is also hard for the OP to see it. So, if somebody posts something in good faith, comes back and does not see it any more, they might also think this is some technical problem and repost the thing. By contrast if they find it closed with an explanatory comment things should be much clearer. In my experience, at some point having interacted quite a bit with them (though lately not so much), a very considerable fraction of users posting completely off-topic things are actually reasonable people, they just did not read the FAQs, missunderstood the intention of the site, missunderstood the FAQs...

Just being told in a clear and non-offensive way what the problem is (of course still closing the question), many of them leave without any additional problems.

I usually agree with Quid's viewpoint. However, I make an exception for things which I think are genuinely damaging to this website, such as crank proofs of famous conjectures. It has been demonstrated here and elsewhere on the internet that cranks are unteachable and need to be dealt with quickly and severely (though politely). Anything less and they won't go away. For example, the author of the Goldbach conjecture post has been asked repeatedly to stop posting but just won't stop.

@bsteinberg: It's common to flag the second occurrence as spam. Since this behavior has only been exhibited in very low rep users, the 100 point penalty doesn't make a difference, so it's not unreasonable. However, please try two other approaches first: communicating with the user (through comments), and flagging for moderator attention.

Flagging spam/offensive has one other effect: a question stops appearing on the home page once it has 3 spam/offensive flags. (it gets automatically deleted one it has 6)

Thanks for these comments. One of the things that surprised me, when I reached 10K reputation and could see a list of items flagged "spam" , was that the list included numerous items that were undesirable in one way or another but did not fit my picture of spam. I think the present discussion, if seen by enough people (and that's a big "if"), should bring the spam-flagging closer to what I think of as spam.

@Mariano, yes it was that one. BTW, I also flagged as spam the third version of the question on Stone-Weierstrass for spheres (the OP was told in the second version to just edit his first version and not repost the question). I must not have been the only one since I don't see it anymore unless the OP deleted it.

@Mariano: likewise.