Unfortunately Lego puts a lot of air in their boxes for selling reasons, so if you have a lot of Lego, the boxes need a lot of space to store. But the box is useful in many ways. For instance:

• To store your parts (and building instruction!) if you break down your model.
• To give away your set to another. It's much nicer with the box!
• To sell your set at fancy fairs, auctions, and so on. Did you know prices can double if the box is still there. For very old sets this may amount to more than 10 times the value without the box.
• If you don't have room to store your box, you can also sell it separately at auctions like Ebay or the famous BrickLink marketplace. There are always people who regret having thrown the box away.

Unfortunately nowadays boxes are no longer sealed (so you could just cut the seal), but mostly glued. If you intend to keep the box, open it carefully on the side with the perforated half circle(s). Cut with a sharp knife between the (mostly glued) cardboard on the bottom and the two sides. And always keep the inner box and inlays (if applicable).