Places like Amazon and Target both have subscription shopping programs—you tell them what you need and how often, and they ship it to you at a discount. They may not always be cheaper compared to local stores or warehouse clubs, though.
Rather Be Shopping compared prices from different online subscription programs and local stores. Things like diapers depend on brand: Luvs is cheaper with Subscribe and Save but not Pampers. Dog food and toilet paper are cheaper online with the bonus of having those large items delivered to your door.
Like most pricing tips, like what's cheaper at Costco or Amazon, your mileage may vary. That's why you need a pricebook—so you know the price of the stuff you buy. Check out the link for one person's shopping adventures with different household staples.
Subscribe and Save: What Items Provide the Most Value? | Rather Be Shopping
Photo by 401(K) 2012.