Jerry is, of course, right with regards to the legal aspect of the matter - it changes from state to state and from country to country.
I don't think it really is legal matters that want to be discussed here, though, but the personal feeling each of us has when they are out in public places, happening to photograph strangers or even wanting to do so.
Some become quite intimidated (myself, too, I might add), others have the confidence to "be in the right, so what can the photographed person say?". I wish I were more daring what street photography is concerned (I only sometimes am, as some of my NYC pics show, but at the time I stepped out of my shoes quite a bit because I was a stranger).
Actually, I did photograph some people in town only on Tuesday morning, but that town is so old and pretty that people are used to tourists taking photos, which changes the situation somewhat.
Therefore I might suggest that those who want to "teach" themselves a little more confidence go to places where it is relatively "normal" that people take photos.
You cannot always FIRST go up to the people and ask them "May I take your photo, please?", for that'd ruin the very moment you want to capture. You need to get a feeling for the situation. Sometimes it feels alright to take the photo (like when I photographed the four guys eating ice-cream in Berlin, they were quite amused by the fact that someone directed her 300mm lens at them), and sometimes you have your doubts, like with that painter in Cowes on the Isle of Wight who was taking a break from work, sitting on the street in his painter's outfit, and I thought this would be a nice pic, I looked at him, ever so slightly lifted the camera, he shook his head equally slightly, I nodded --- and that was it. No photo. He very obviously didn't want to be photographed. I had to accept that.
I also remember the situation of the young oriental couple with their baby boy in the park who could only JUST about walk. He still staggered in the way toddlers do and looked really cute. I took his photo and they saw me take it and never either came closer or said anything to me or grabbed up the boy and left or anything ... so I took that as their silent agreement that they were ok with me taking a pic of their baby boy. I guess they even felt a little proud that a total stranger found their boy cute enough to be wanting to take his photo.
As you can see, the situation can vary a lot.