I only recently started really collecting Legos and this is exactly what I've been doing, too--get rid of the smaller boxes, and break down the larger boxes and store them flat!
I am starting to accumulate new, unopened boxes due to clearance and sale pick ups, so I'm not too sure what I'm going to about those in the interim before I build them.
I'm interested to know where people store/display their legos in general...not just the boxes...