For anything that needs to be folded, consider installing pull-out baskets — like this Komplement Mesh Basket With Pull-Out Rail ($20) — and assign a basket to each person in the house. Have everyone be responsible for putting away their own folded laundry.
To make things even simpler, set up baskets that can pull out completely and be carried to bedrooms, like this DIY laundry basket dresser. When all of the folded laundry is put away, these pull-out baskets can slide right back in place so they're ready for the next load.