I keep them on the attic shielded from dust. Because:

a.) If I want to store the figures

and

b.) If I ever want to sell them, the original box is a big plus

I keep mine because they're easily resealable, so they're worth keeping for storage/resale purposes. It's not a space issue for me, since I only have a handful of them.

For Figuarts, Figmas, and MonsterArts, I have them on bookshelves in a closet. I want easy access to them so when I want to switch out their accessories I can.

For American toys like Marvel and DC, unless there is something special about the box (like Doomsday), I toss them out.

Since I keep the accessories in those trays, I don't need access to the boxes, they're on storage shelves out of the way, or boxed up in bigger boxes.

http://i.imgur.com/0OZx8QE.png
http://i.imgur.com/OLoojQQ.png

http://i.imgur.com/dawwptS.png
http://i.imgur.com/EPJM0kK.png
http://i.imgur.com/xvPNRZ0.png

I have an entire wall of Toku boxes in my room

ATo be fair, I live in an apartment, so even if I did have them in trays, I would still have the boxes on book shelves since I would have no where else to store them.

I bought a few of these plastic shelves from Walmart, think they were $30 each or so, you can fit a TON of SHF boxes on them.
the standard SHF boxes fit 2 high and 2 deep, so you can fit about 60 boxes on one shelf.
(click for full size)
http://ryanlb.com/images/misc/shf-box-shelves.JPG

they're a pretty decent use of space.

It took me a moment to figure out the orientation of that pic...

if you view the image directly it's correct, there must be something strange going on with the code that resizes the image. :/

Just click the image to view it correctly.