I can't believe you'd post such a topic without just asking Kevin or I
Anyway Beowulf is right about the Long Halloween being the definitive Batman Detective story. Year One and Dark Knight Returns are known for how influential they were to the entire comic genre (i.e. comics can be for adults), but the Long Halloween is good because it's simply a good BATMAN story (i.e. detective work, kicking ass, etc.). Year One and Dark Knight Returns influence could have been achieved via a different character imo (i.e. Animal Man, The Watchmen, etc.). Batman was not an essential part of it.
As for other Super Hero related titles, I agree with Lantis in that anything Geoff Johns and Green Lantern is golden. Rebirth
is where things start, but his entire run has been going for over 6 years now and been great. I am however hesitant to recommend this since it requires knowing SOME background. Anyway if you told me 7 years ago that I'd A) be reading Green Lantern and B) that it'd be the best book I read month after month, I'd have laughed at you.
Another great super hero comic run was Joss Whedon's Astonishing X-Men run
. I think it's ~24 issues and 2 or 3 trades and just a great read (even if it is super hero). I have a feeling you'd like it the most out of anything super hero that I recommend.
If you're not into Super Hero titles (as you mentioned), I'd recommend my favorite comic book Midnight Nation
by J. Michael Straczynski or The Walking Dead
by Robert Kirkman. The latter has a new series on AMC, but after two episodes I prefer the comics quite a bit more (which isn't to say the TV show is terrible...just not as good as the actual comics).
Another Warren Ellis book that's solid (and short) is Global Frequency
. Don't read ANYTHING main stream super hero by Warren Ellis though. I found his X-Men run to be ATROCIOUS.
...oh and you could always just ask me to bring stuff over next time I visit. As long as you return them in a reasonable manner of time I don't mind. All the things listed I own
. Anyway that's the stuff that comes up off the top of my head. I'm sure I can come up with more if need be.