I keep the boxes, but don't believe that it adds to the value of any firearms I have. Now, say a 1950's Smith and Wesson revolver with original box, that is a different story.
Yes I keep everything that came with the gun and look for the same when making a private purchase. It’s not so much that it adds value for me but it shows me that it has a clean history if the packaging has matching serial numbers. Not saying that someone who broke into a house and stole some guns wouldn’t have a box but it’s highly unlikely they would take the time to search the house or garage for the empty box and match up serial numbers. I have in the past bought some rifles without the box but they were more along the lines of mil spec surplus type.