On-Topic: Anything that good hackers would find interesting...anything that gratifies one's intellectual curiosity. Off-Topic: Most stories about politics, or crime, or sports...
Speaking personally, I love reading about EFF taking the US government to court, which is politics. I also love reading about the technical advancements in Formula 1, which is sports. Sports and politics, yes, but also very gratifying to my intellectual curiosity.
Here's the thing: I wouldn't want to see them on Hacker News, because I can (and do) get them elsewhere. This particular community gives me things I can't get elsewhere, and I love it for that. I don't want it to become another Reddit (or even another Slashdot, or Digg, or Gawker, or TechCrunch, Cracked, Metafilter, or ZDNet).
Hacker News is not (yet) a general purpose "news for nerds" or "all your internet goodness curated", and the longer we can stave off its descent into the general-purpose semi-curated things of somewhat geeky Internet interest, as every other good site of any age seems to have descended to, the better.
(http://ycombinator.com/newswelcome.html)
> A crap link is one that's only superficially interesting. Stories on HN don't have to be about hacking, because good hackers aren't only interested in hacking, but they do have to be deeply interesting.
> What does "deeply interesting" mean? It means stuff that teaches you about the world. A story about a robbery, for example, would probably not be deeply interesting. But if this robbery was a sign of some bigger, underlying trend, then perhaps it could be.
> The worst thing to post or upvote is something that's intensely but shallowly interesting. Gossip about famous people, funny or cute pictures or videos, partisan political articles, etc. If you let that sort of thing onto a news site, it will push aside the deeply interesting stuff, which tends to be quieter.
EFF taking US Government to court could fit here, because it doesn't have to be partisan politics, and it could be a deeply interesting discussion of legal process. I've learnt a lot about US law from contributors here. "Vettel Wins" is sports, "Redbull use X to help Vettel win" is probably tech.
I agree about not wanting to see them on HN; while they could be discussed well and in conformance to the site guidelines they're usually not.