When I was young my mother used the technique of cutting out the front and back and thus preserving the various ideas that the photographs of the set provided. She stuck the box bits into a large craft book and it was stored on the bookshelf; it was handy to get to and flip through. Don't do this; don't go cutting the front and the back off. Whilst most of the interesting information is only on the front and back, the economic value of the box is destroyed when you cut it up like this.
If you want to resell the LEGO as a set later, having the original box greatly increases the value of the set. The boxes for certain Technic sets can achieve values of $50 or $100 - just for the box.
The best way to preserve a LEGO box without it taking its full volume is to use a box cutter to cut the glue that holds the flaps onto the sides. This preserves every visible surface of the box and allows you to reassemble/re-glue it at some point in the future. Cut down like this the box takes up a fraction of its original size, and can be stored in an out-of-the-way place like an attic or on top of large shelving (be aware that a box cut down like this can be surprisingly large and unwieldy). Don't stack too many boxes atop each other like this - cardboard is both heavy and floppy, and searching through a substantial stack may require more strength/space than you have available.