Many military people do feel a sense of duty, and that's why they serve or served. In a civilian sense, duty would be things like acknowledging that a park is a shared space. If you walk past a piece of garbage and don't pick it up, you have failed in your duty to maintain the shared space even if you aren't the one that dropped it. A contemporary one would be cutting down on CO2 emissions. It's everyone's duty to cut back on that; someone who bought a Hummer would be shamed, as would people who keep their thermostats super high or low. Gossip spreads that you're a clod who's damaging the environment we all share, and you get shamed.
People used to patch potholes in public roads near their house because they felt a duty to keep the neighborhood nice.
These things don't happen anymore. I'm not sure whether that's a good or bad thing, since there were certainly downsides to duty. I don't even know if it's legal to patch potholes in public roads anymore.