Friendly Creatures can be silenced, but so will your footsteps.

Under 'Options > Music & Sounds' there is a slider to turn off the sounds that peaceful mobs make.

A cow's moo and its heavy footsteps are silenced, and that's great if you have a ton of them nearby. But you also lose the ability to hear a your own footsteps, or even a Creeper's steps from behind! (Not a very friendly mob, mind you...) Blocks like dirt, gravel, and sand don't make a sound when walked upon or while being mined when peaceful mob sounds are set to 'OFF'.

This is a bug that constantly has me switching between having this setting on and off.