Put shelves in the closet. Low ones preferably, since these are more accessible to them. The shelves allow for more to be stored in the same section of the floor. I like it to be in the closet, so the door can be shut and then fewer things are visible in the bedroom. If you keep the shelves low you can still hang clothes since children's clothing items are not as long.
Divide Toy Parts. My girls collected a lot of Littlest Pet Shop pets. I think they have nearly 125! Originally, we stored them all in the larger bin below. Over time, the pets and accessories they come with filled the bin to the point we couldn't close the lid! So we brought out another smaller bin to contain JUST the pets. They liked being able to get just the pets out with out digging through the accessories to find the one they wanted.
Use bins with lids. As you can see, we use bins for different of type of toys and keepsakes. The bins give a defined space where we store the toys. The provide a limit to how much one can keep, too. Add a lid to the bin, and several bins can be stacked in the corner of a closet or up on shelves for adults to retrieve when it's time to play.
Hide under the bed. We use the space under the girls beds to hide and store toys. We use bins too. Those shown above are wide and long but not very deep. I think we sometimes kept the lids off and stored elsewhere. They slide out easy. They contain the items so they don't get lost under the bed to never be found again.
Games Stacked. We stack our games on shelves. All in one place. And never in a bedroom. Games have usually been stored on shelves, sometimes in a hall closet or in a basement. You might notice I even corralled small games, like decks of cards, in a bin. At this point we have several games that are are for children younger than my girls, but a few games like this are nice when we have younger guests at our house.
Store up High. I would highly suggest some children's toys be stored up high. It's not necessary for older children, but toddler shouldn't have access to craft supplies without supervision. Storing those types of items up high helps keep them out of reach, until an adult can assist. We kept our craft supplies together in one place. Back when they had much more, we would have various containers to keep things all together. As far as the toy sets, I put those up high because usually the highest shelf has more space above than other shelves. In this case the lower shelves wouldn't accommodate the size of the toy.
I hope you noticed from the pictures how much we use bins and group like items together. That is key, regardless of where you actually store the items. The less your children have, and the more contained items are the more organized your child's room and toys will seem. Trust me!!
Do you store anything under beds? Do you have extra shelves in your closet? Are your child's toys stored in bins?