I use all kinds of things...
I have an 'issue' with plastic bins. LOL I do use them, but they have to be stored out of sight, like in a closet. So we have some legos in plastic bins, GI Joes etc - but they are stored in the bedroom closets.
My sons are older, so stuffed animals are not around the house anymore, but when they were, I had a big willow basket just filled to the top with them (it could stay in the bedrooms since it wasn't a plastic bin LOL). Both my kids have these net tubes that I got at IKEA. They hang from the ceiling and have little holes to tuck things in...they don't use them for stuffed animals but they could be used for that - gets them off the floor, out of the way but you can still see them.
Here is a pic of the 3 shelf one...we have the longer ones with at least 6 shelves:
IKEA | Organizers | Children's small storage | MINIFĂ…NGST | Hanging storage/ 3 compartments
Both my kids have two bookcases in their rooms...a tall one and a short one. So they work great for all their books. I also use some fabric bins to store small items like decks of cards, box of marbles...stuff like that. They're contained but out of sight and the fabric covered bin looks nice on the shelf.
They also have shelves in their closets...so I use some plastic bins and fabric bins in there as well to corral things.
They each have desks, so all art/school type supplies are organized in the drawers of their desks. I don't use bins so much for that stuff, but some cups with colored pencils in them or markers. Those plastic trays keep things together in one place etc