I started my kids with yarn and plastic canvas to introduce the idea of how to use a needle. Then My daughter sewed a little stuffed animal from felt - easy shape like a cookie cutter, and I marked dots for her to put the needle through all around the edges. Then we moved on to tracing and cutting squares of fabric and sewing them together by hand. I also traced some designs onto plain fabric that she could embroider, and that went pretty well.
Felt is good because it doesn't ravel.
Like others have said, it depends on the child and their attention span. My son hasn't shown nearly the interest that she has, and so hasn't actually completed any projects. My daughter made a little doll quilt (I sewed the long seams on my machine, and bound it, and she used yarn to tie it) when she was 5.