my favorite circumstance under which to whip is when i first discover gunpowder, and i dont have the cash to upgrade units, or just simply dont have the time to let the muskets come naturally.
i generally play a fairly peaceful ancient/classical age, and really kick myself into gear with knights and muskets (as far as war is concerned). i always seem to get myself in a population bind right about this time, and so whipping helps alleviate some of the crowding tension.
im playing a weird game right now where my whole continent (huge map, 15 civs, 8 civs on my continent) have converted to judaism, and i havent had to go to war a single time...everyone is friendly to everyone else!!! i have a definite tech lead over all but one of the nations i live near, so i have decided to smash all of my neighbors but one (isabella is the nation that is near me in tech, and i dont dare incur her wrath this early in the game, until i have the loyalty of several nations).
so.......i have whipped trebuchets in half my cities, and muskets in the other half, in preparation for capitulating the whole dang continent around 1600 a.d. or so.
ill post an update to let you guys know how it went