It's situational. There is an issue with car break-ins in the neighborhood, so no, I don't trust people to not break into my car if I leave things visible in it. That's probably the low point of "do I trust my fellow citizens?" And it's only a small number of people who are responsible for that lack of trust.
I do generally trust my fellow citizens to not harm other people. For a city with a reputation of being somewhere between Detroit and Toronto on warpus's scale, it feels a lot more like warpus's hometown than I would have expected, even late at night. I'm not sure why exactly, but I think part of it is that the local area has that neighborhood people-know-each-other feel, and another is that people feel things have been going the right way in the city the past few years, and many feel that they're part of that.
It probably helps that I don't follow the local crime blotter, but know a lot of people who live nearby. I think that has an impact on trust as well - watch the nightly local TV news in the U.S. and you may think the whole city is a dangerous war zone, but go out and live in it and you may find that significant parts of it are actually pretty nice.
Could you imagine asking anyone who waves at you for the money to get you through the rest of the month? Such things used to be done, but this is well beyond what could be reasonably expected today. You'd be thought a loon to even ask.
IMO the key difference is that, if we assume that such things indeed used to be done, it was often in a small town where everyone knew (figuratively or literally) everyone. It wouldn't be a random person who waves at you, but Joe the factory worker that you play basketball with every so often who just got laid off. You've known him for years and there's a pretty good chance he'll find a new job soon. In a big city, you probably don't know any random person who waves at you, and even in 1950 that wouldn't have been the case.
Things aren't necessarily the same today, there aren't as many factories where Joe can get hired on. So it may well be more case-to-case.
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As for the honesty box question, I've seen them in Ohio. I think the last one I saw was even in the City, on someone's front lawn in one of the nicer City neighborhoods, where there was one lonely melon left for sale, so either someone stole a lot of melons, or it was working as intended. I wouldn't try it right outside where I live as it's too prominent of an area, but I would in certain locations, including pretty much all of rural Ohio.