If you are planning on shooting on location, you should always check to see if you need permission before you show up. This is particularly important if you have a crew of more than 2-3 people or you are shooting drama. Generally locations fall into two categories: private and public.
Private locations - in almost all cases you will need permission to shoot on a private location. It is important that you get the location owner (or an authorized representative) to sign a release form giving you permission to use the location. You should also make sure you have the necessary insurance to cover your cast and crew, and you will generally have to indemnify the owner against any claims arising from your use of the location. Using private locations may or may not involve a fee, this really depends on the circumstances and your persuasiveness.
Public locations - in most cases, you can shoot freely in public locations, however you should always check first with your local authority. If you are planning on shooting in a busy area or with a reasonably large crew, you will often need to obtain Police co-operation for things such as crowd and traffic control. Again, depending on the individual situation, you may be able to obtain this at no cost. Crowded areas or popular locations will always be more hassle to use than quieter ones. Be prepared for the shock of rules and cost if you want to shoot in places like New York City or Central London.
Many cities and regions have government sponsored film commissions whose job it is to promote their locations to filmmakers, and help arrange any necessary permissions to shoot. Check out the Association of Film Commissioners International, a global organization whose members include film commissioners in a range of cities and countries.
And as a final note, when you do get permission to use a location (public or private), make sure you leave it in better condition to which you found it. It is very easy for a film crew to trash a location (and owners are well aware of this) and you will be helping other filmmakers and ultimately yourself if you take very good care of your locations.