you want the chain to move at LEAST a half inch total, back and forth when pressing and pulling on it in the center of the chain. when you're stopped, you want the pedals to move a small amount. the amount will change depending on your gear ratio and how much slack you actually have.
if you're running a 1/8 chain and cog and chainring you'll be just fine if you have as much as an inch or more of slack, even if the pedals move a ton while tensioning the top or the bottom part of the chain. if you have 3/32 components or you are using a ramped ring, you want hardly any slack at all. a track chain and track components won't derail even with tons of slack, say, two inches total. a ramped chainring and an 8 speed chain will derail at the slightest provocation with even a half inch of slack.