Whether or not to shove all-in with KK or lower pairs depends on many factors. You should even fold AA sometimes.Every situation is different.
In cash games, just ask if you're willing to risk your whole stack, and are you confident that your opponent (hopefully there's only one) doesn't have AA. For me, if an opponent is being unusually aggressive preflop and I have KK or lower pair, I fold.
In MTT, blind structure/ speed and stack sizes (in a turbo definitely shove because you need to keep making chips),what stage of the tourney it is (bubble/ICM pressure?), tendencies of(tight, loose, etc.) and number of opponents, whether or not you are able or willing to rebuy.