Creating a master list of common staples that you find a family member uses the last of - but then never tells anyone - can be a timesaver. On your fridge, post a list of common items your family tends to either go through quickly, or frequently used items that you never think to check unless someone says that it is all out.
Here is a list of frequently found items on the grocery list
Milk
Cereal (might want to do a couple specific kinds)
Ketchup
Mayo
Salad
Bread
Orange juice
Juice boxes
Fruit snacks
Popcorn / snack food
Also, make a penalty for people who use up the last of an item but don't mark it off. It can be something like no TV that day, or skipping a coveted trip to McDonalds or the video store.
