The question I get most often is “How do you handle shooting people? Should I ask permission or just take the picture?” This is a tough one and depends on so many things. In a public space like a street, square, festival or park I think it’s usually OK to shoot people without asking, up to the point where you are getting into their space or shooting something that might be embarrassing. This would depend a lot on local culture and norms. It might be much more acceptable in a European country, for example, than in a Middle Eastern country. Also be sensitive to the camera fatigue that many people must have when tourists and travelers find them interesting and shoot them all day long.
Sometimes you just have to be a little sneaky. One of the things I like about the newer mirrorless cameras is that many of them have a truly silent mode. The camera makes no noise at all which makes shooting unobtrusively so much easier. The flip screen on many cameras helps even more, allowing you to keep your eyes off the camera. I frequently line up the shot and then look in another direction, using my peripheral vision to wait for a good arrangement of elements before pushing the button.
The safest thing is to ask permission and then live with the answer. One thing I am against in almost all cases is paying money to shoot someone on the street unless they are a performer or you are on an organized trip and know that tipping is part of the deal. Paying people for pictures just perpetuates an unhealthy relationship between traveler and resident that dehumanizes both. Just my opinion.
Large public events are, of course, great places to photograph people. Not so much for the front-facing parades and shows, but for the behind the scenes chaos and moments that happen whenever that many people are in one place. The last photo below of a family unwinding after the official ceremonies was shot in Oslo during Norway’s National Day. There are so many cameras around those kind of events which gives the more serious photographer (you!) more freedom to shoot what looks interesting.