It depends upon many factors: how many civs there are, how close to you and each other, respective religions, etc. Typically, I play with only 6 civs on a series of continents. If there's a large space between civs and I build a respectable military, no one will ever declare war on me.
But it also has to do with which civ is near you. Montezuma will invariably attack as soon as possible. Genghis Khan expands like mad. Tokugawa will stab you in the back at the first chance. Isabella will come after you if your religion differs from hers. Others civs are more peaceable.