I keep my boxes depending on the product. Mainly, I keep all my Apple boxes or boxes for expensive electronics as they help resale. But I don't keep boxes for headphones, house phones, etc.
That being said, I don't keep them for display either. They're up in my closet.
The boxes I currently have are:
MacBook Pro
iPhone 3GS
iPod Touch
iPod Nano first gen
iPod Mini
some boxes for motherboards (motherboards often come with a bunch of extra crap and cables you don't need so I just stuff it in those boxes).