in a couple bins, labeled it and put it in the attic. When they get a house of their own we will give it to them to hold on to, reminisce or pitch.
My parents did that for us and I have held on to a lot of it still. Showed my kids stuff I did as a kid and they were really interested in knowing what their dad was like when he was their age. It certainly provides the opportunity for connection. Sure, they hear the "when I was a kid" stories, but when they see your artwork, hold your trophy, look at your report card, play with your toys it can be special.
My wife and I are probably more sentimental than most so we have held on to alot; but the reality is it takes up less than 5% of the attic ... so it isn't really costing us a thing.