The answer depends where and when. Various Italian states denied (or attempted to deny) France and the Holy Roman Emperor access to their territory, typically if they disagreed with the war but did not want to get involved. This mandate was ignored at the risk of opening an additional theater of war; a strong enough army could simply march through or even invade, or the general/prince could pay for passage. The former happened to Milan on at least one occasion.

Elsewhere, however, territorial boundaries were completely ignored. The example that comes to mind for me (as an early modern German historian) is the Thirty Years' War, where armies from all over Europe marched and pillaged through German lands with impunity.

Basically, whether or not armies ignored borders depended on whether the general felt confident that he could pass through the territory without angering an enemy formidable enough to hurt his war effort.

Sources:

Thomas Brady, German Histories in the Age of Reformations, 1400-1650

Peter Wilson, The Thirty Years War: Europe's Tragedy