Let me start by saying how sentimental I am about this stuff, but it's just not feasible for us to keep everything, so...
-Filter some out to grandparents
-Definitely scan, take pictures
-We put some of the more unique things on DS's wall near the ceiling as a border
-Frame some of the favorites, they look really nice as actual art
-Use those digital images to make personalized tote bags, playing cards, etc. on a site like Snapfish, Shutterfly, etc. I'm considering making a photo book of all of DS's art until now. If you're on a budget, just print it out on transfer paper, and you can do some DIY bags, pillowcases, etc.
Have fun!!
I do end up tossing some of the regular projects (how many collages do we really need?

). It's heart-wrenching, but you're right, you'd have to build a new wing onto your house to store everything your babies made!!