Give it to the grandparents. That's what I do! I realize this may not be a solution for everyone. I have a 4 year old preschooler, who creates a massive amount of paper projects between church and school. Since I'm a self-prescribed 'organized-hoarder' I had to figure out a way to deal with all of Nathan's schoolwork and projects.
A while ago, I sorted through a bucket of every project I had saved. I pulled out what I wanted to personally save as keepsakes, then I sorted out what would go to the grandparents.
I labeled baskets with tags for each set of grandparents. (I'm in love with this font, strangely named 'Rage' - if you also like it, you can find it for free at Kevin and Amanda's blog.)
I sort through Nathan's schoolwork and projects as I collect it. I set aside what I want to keep and toss what I think the grandparents would like into their respective baskets.
I also keep a handful of large envelopes in the baskets and the baskets literally sit on top of my desk credenza. This makes it very convenient to pull a basket down, grab an envelope and gather some items together, address and send off!
This works well for out of state grandparents (like ours) who don't have the opportunity to interact with their grandchildren in person much. I feel like it's just a small way to include them in the life of their grandchild. I also throw less away, total win for me!
For grandparents who are not out of state, this could still be a useful way to share all those paper projects, Get the kids involved in putting together a grandparent packet. Mail it or hand deliver, either way is fun. If grandkids saw some of their work displayed on Nana's or Papa's fridge, they just might feel extra proud!
Just something that's worked for me...