As a photographer, professional or not - remember not to forget the element of surprise when taking pictures in the street. It's all legal, shooting people, buildings - even the grafitti, whether considered street art or not. Your free to shoot, but just respect people at all times that's all - you can't go wrong. In principle grafitti is illegal (unless it's authorised, though remember hardly any of it ever is)
Copyright only applies if it actually is and that's the point - most isn't, so let your imagination and your camera roll! And on the subject of copyright, most national monuments and listed buildings actually are - so remember that next time you shoot pictures of the Eiffel tower. Although your not likely to find an official looking for a fight, that is unless your in the business of advertising.
*info applies to France and the EU, for the rest of the world - check your rights first!