Here are a few ideas for saving their creations:
Poster Portfolio: Take two large posterboards for each child. Punch holes 2 inches apart along 3 sides of both posterboards. Using yarn, lace the two together leaving one side (the one without holes) open to create a large pocket. Label the outside, and store all artwork flat inside.
Art Binders: These work best for all of the flat artwork as the dimensional pieces may not flatten enough to fit. Decorate a binder specifically for each child. Then 3-hole-punch each piece of art to add to the inside. You can go further by using page protectors.
Under-the-Bed Boxes: The plastic storage containers made for slipping under the bed are perfect for storing artwork. They are roomy, convenient, and durable. Storing it under the bed of the artist is a bonus as they won't take up any room in common spaces.
Digital Storage: Scan or photograph each piece of artwork. You can toss the original, or store it in one of the above ways. Then use the digital image to create a work of art themselves. You can find some brilliant ideas here, here, and here.
How do you store your kids' works of art without cluttering up your home?