Could we share our experiences with cities in general here? Would be great to be able to check before heading somewhere. So far I've been learning through this thread that Netherlands could get a lot sketchier than I thought.
I'll start- there are just my experiences and I can't comment further than what I've experienced. Some people might have had a different experience in the same place, and I could be wrong.
Japan- from my experiences, Tokyo is safe at daytime. I ran around with a 1675 or 69 speedy. But when it got to night I've been told Shinjuku or Akiba can get sketchy so I wasn't really around at night, and if I were I was just wearing a vintage Hamilton. Kyoto and Osaka I went around at daytime with a ST1. Not much happening. But at night I didn't risk it.
Korea- Seoul is safe at day and night. I've been told certain areas in Seoul could get sketchy at night, especially the west parts. I haven't ventured there at night to find out. But also, yes crime does happen rarely around the east areas too, it's not like crime rate is zero. But a little common sense would help you to keep you out. Obviously though as others have said, luck is a huge factor and it just might happen to you (sh1t happens)
UAE- I was out in Abu Dhabi at day and night with a SM300 nodate, 5513. I had no problems, presumably because of the government's strict laws on theft, but also I didn't get looks as much as I did in other places with the SM300 there. I got the feeling people didn't know 5513 there too.
US- NYC I get the feeling that certain parts of Manhattan are pretty safe at day and night but I wasn't out with a Rolex. Just a speedy once in a while. Once I was in upper Brooklyn photographing through late night but that time was winter and I had a Hamilton under my wrist. Luckily it passed, was it just luck or awareness etc, not sure. I haven't been at other areas of NYC at night to find out. Most of the time at daytime I was out with a Hamilton. Other people would be more qualified to comment here..
Other places of mention. When I was travelling Egypt and Uzbekistan with my SM300 I got the feeling people didn't really know what I was wearing. Maybe if I was wearing a Rolex it would have been different.. but to be fair this was fall/winter and it was always under sleeves.
I largely agree that most of it is luck/chances but also that you can always help yourself to not let it get to 100% chance of getting robbed. In general though after writing this all out I think I was pretty lucky. Seems like I was a pretty dumb person doing all this.