Like many above I too used to keep all boxes including the plastic on cards, but eventually became useless as I'm not really gonna sell any of it. Even if I did there's tonnes out there (modern figures that is) that are MISB anyway.

I've pretty much just kept the cardbacks and card plastic inserts. For boxes I throw away the interior cardboard and just keep the actual box folded flat.

I do keep a select few packaging. Special Editions, great looking and hard to come-by packaging. All my TFA packaging will stay though.