I throw it away. It takes up less room that way.
I've always wondered the same thing loll, I keep my opi mini's in the packaging because I think it's quite cute, but with bigger sets i just throw them away ! (btw. good luck with your exams next week)
I keep them, especially the color club ones, for packaging polish in for swaps and sales.
I throw them away, but most of my polishes come without packaging.
I throw most of it away but there are some boxes I do save. And I save bubble wrap, especially the bubble wrap pouches with the adhesive.
I usually make labels for the polishes first and then throw away the packaging for the Color Club sets. It's a hassle to store them in the package.
I have nail polish racks in which most packaging doesn't fit. But I can't bear to throw them away, though, they're way too cute! Therefore I store them in a box. :)
I generally get single bottles. I don't have much packaging to save, mainly just packing materials like bubble wrap. If I buy a bunch they may come in those little cardboard shipping "crate" type boxes, and I'll keep those for reuse of shipping. If the packaging is elaborate and takes up too much space it's gone. But I like it when mini bottles come in plastic "sleeve" type boxes - handy for keeping a set separate from all my other mini bottles.I will say I'm huge on recycling so if it's anything that can be used for organization or later shipping, I save it!