This is by far the best playdough recipe I have come across.  It will last for ages.  I don’t keep mine in the fridge.  If you don’t have cream of tartar it will still work but probably won’t last as long.

2 cups flour
1 cup salt
2 cups water
2 Tablespoons oil
4 teaspoons of crème of tartar
Food colouring

Cook in a pot on medium heat for 3-5 minutes. 

Store in an air tight container.