Just Pure Lovely shows how she transferred her child's drawing into stitchery. I think this is one of the most fun ways for kids to get started on stitchery. For the youngest, have them do the drawing then you do the stitchery. Either way the results are always worthwhile!
JCasa Handmade has a super felt board tutorial made from a stretched canvas. Give it a try and have fun creating all the felt shapes for your child to play with. This would be adorable hanging on a wall too with changing scenes :)
Resurrection Fern has a simple tutorial on how to make these birch bark vases from empty jars! Recycling at its finest! These would make such a lovely addition to your nature table and they are so easy to make.
Obviously I love ideas that combine children's artwork with sewing and when it creates a usable object it's even better! Mary Tree shows how she created these adorable pillows with her children's drawings here. **Edited to add: check the comments here for more details from Mary.