My D&D group decided to run "morally apathetic" characters. I was a bit skeptical at first, but they've actually don't a really good job. Good backgrounds, hidden goals, consistent and developing characterization, etc.

I set them up with a political intrigue adventure first thing, which was a bit of a gamble, but well worth it, since it's forcing them to emotionally invest in the setting right off the bat.

@Sololoso I feel like Id always be catching myself being a bit too railroady with that, have you had issues with allowing them to play their PCs versus involving them in stories?
@CFHistory I won't lie, I've been nervous about it, but apparently they don't feel forced in any particular direction, they're just interested to see what's going to develop. I DID give them a gentle push in the very beginning (with a hook added in), but otherwise they've been pretty cooperative. Any gaps in my preparation have been fairly simple to improvise-- well, other than when they latched onto a baron's embezzlement scheme for an oddly long time.
@Sololoso Its always important to gauge what your players care about lol. That's super cool though!
@CFHistory What I definitely didn't expect was the apparent violent anti-monarchist streak in the party's tank/assassin. I had assumed the anti-monarchist faction would be a passive antagonist (and wrote several encounters in that vein) buuut... hah!