Well, Augustus prided himself on closing the gateway of Janus Quirinus three times in his Res Gestae. They were only closed in case of 'world peace' Of course that only goes for the world known to the Romans at that time, and their definition of world peace isn't entirely clear either I think. But I'm sure that if they only declared such a period 3 times during Augustus and 2 times in the entire period before him they didn't declare world peace to lightly.
Res Gestae Divi Augusti (Achievements of the Divine Augustus) section 13
Yes, I've heard of that. The duration of each peace is much more important than how many peaces were declared, though.