Of course most of the time it is legal, you do have the right to snap people on the street.
There are of course exceptions, e.g. sensitive installations where no photography whether of people or the surroundings are not allowed.
That said, there is law of street, if the Big Muscular Man punches you because you are shooting his Quite Pretty Girlfriend non-stop (which quite some "street photographers" seem to indulge in) and following them around, I guess you can't really blame him. Of course the law doesn't allow for his punching of you, but what for invite trouble? Practise due-discretion.