Hi, H..
I use a vertical file system. I purchased a letter-size file (like the kind that is used in many office situations) for each child and myself, and mounted them all on one of the walls in our kitchen, where everyone can see them as they enter the house from the garage. That's where we store all the projects/homework that they're currently working on, paperwork on field trips, etc.
When there's a form to be signed, etc., I sign it and put it in the child's file. It's the child's responsibility to make sure the form makes it from the file back to his/her backpack and back to school. This doesn't always work, but it's a great way to teach responsibility with naturally occurring consequences!!
Be sure to give yourself a file as well, for paperwork that is more general school-related and not related to a specific child's classroom.
For all the work and projects that come home, I try to deal with it right away. I assess whether I think it's the kind of thing that should be kept as a memento/sample of their work for that year. I put the keepers in one pile and the tossables in another pile. Then, just to be safe, I have the child go through the tossables in case there's anything in there that they really want to keep. Whatever is deemed a keeper gets stored in a bigger bin.
Now that I've learned how to use Shutterfly, I'm planning on putting together a photo album for each child for each grade of school, so I'll probably take photos of the keepers and put them in the albums. That way, I can toss some of those keepers. But, I know there will be keepers that I won't be able to toss. Those I plan to put in one large box per child -- the kind of box that can slide under the bed. If THAT box gets too full, then I'll work with the child to weed through it.
Another idea I heard was to limit the keepers to one special item per year of school. That sounds reasonable to me. That way, assuming they're all 8.5x11 inches, they could each be slipped in protective plastic pouches and stored in a three-ring binder. One binder should be big enough to hold one project for each of their school years K-12. Once their in college, they're on their own!