Is it bad to apply to multiple master/PhD programs in different universities? I have heard that it is impolite and improper to apply to a masters/PhD program and ask more than one professor at that university to be your supervisor. In other words, when you apply to a single program, you should have determine who you want your supervisor to be and apply upon the prospect that if that professor doesn't want you/need you, you will need to apply again at a later date with a different supervisor.

What about applying to different institutions at the same time however?

Would it be harmful in any way to apply to programs in different universities, either on the same country or internationally?
Actually it is good to do that. You want to maximize the chances that you get in to a program that will work for you. Applying one at a time means that it could literally take years to get accepted if your top choices don't accept you. 

Don't waste people's time with superfluous applications, but definitely apply to places that you find attractive and that you think might find you a good candidate. 

Whether you need to pick a supervisor as part of your application depends on both place and field. Do that if you must or if there are attractive opportunities, but keeping your options open might be a better choice if it is possible to do that.