I do quilling (paper craft). So:
Basic quilling tools (I have at least 2 of each, in case something happens to one).
Paper (I like having every shade of quilling paper I can find. Also other kinds of paper are good as well, because I need background paper to mount my work on. I also have odd kinds of paper - lokta, and handmade papers, these are good for those flashes of inspiration that wake me up at 2 am).
Glue (I buy multi packs of Elmer's - I must never run out)
Scissors (Just for cutting as well as decorative edged ones)
When you do a craft, sometimes you don't use something for years, and suddenly you think of the perfect use for it. It makes the craft area of the house kind of exciting, and sparks my creativity.