To be a spontaneous crafter you will need to establish a stash. You need to have enough things on hand to provide choices while crafting but not so many things your spouse kicks you out. It is a fine line and one that is fun to push up against.
While looking for things to stash you want to keep a few categories in mind.
Staples: What are the staples of your craft? If you do a lot of quilting you are going to want to stash muslin and solid colors in your favorite pallet. If you do a lot of knitting, what is your favorite colors and weights? What are you always wishing you have more of?
Versatility: What kinds of items can be used again and again in different projects? Things like beads, buttons and ribbons have a ton of applications and are great things to stash.
Finishing bits: What things do you need to finish projects? Things like pipe cleaners for knit softies, googilie eyes for kids crafts (why only use two? Seven or eight look better), Velcro and fasteners should be stocked up on as well.