Realistically, the only purposes of a box is to protect the toy from factory to home and to make the item more appealing on the shelf at the store more appealing than the competing item sitting right next to it.

For me there is an unfortunate side effect that there is nice artwork on the box, maybe a bit of a bio or tech specs. these latter two elements aren't half as well done these days as they used to be and the globalisation of box art sometimes makes it a lot less nice than it used to be. but some modern boxes are stunning, well built, and border on being their own form of art.

I tend to keep the card from retail transformers removing all the internal packing and flattening them. if packaging in a line is identical, some legends lines for example, then I'll only keep one. I don't display them though, they are packed away in boxes and stored. Last year though, my hoarding of boxes meant I was able to do some high density scans of some box art for submission to the guys making the Legacy art book, I don't think any of it was used but it was cool to be involved at the time.

I keep all MP boxes and a lot of Special edition or more rare boxes in their 'as is' form and it takes up a lot of space. I do keep not on display MP's in their boxes, and some other figures as well. I need to go through the few 3rd party boxes I have and get rid of their boxes because they aren't often actually that nice and they are massive for the size of toy they contain in a lot of cases.

I don't have to cull yet but I can see myself getting to that point in the future. I'm currently re-jigging my instruction storage solution as it's becoming unwieldy, especially with all the differing sizes of instruction sheets.

I tend to keep not on display main line toys in plastic zip locks in plastic bins.

<edit> And then there is the 'box' from the 2014 SDCC dinobots set.