I save boxes.. Not a lot, but mostly the beer case size. Most of them get filled with outgrown clothing from my daughters.. They are then passed onto our niece. Others are used for those purging binges that result in carloads to Goodwill. It's not like I have a room full of empty boxes... usually, just the jacuzzi tub in the basement. (Lived here going on 19 years, and have used the tub 6 times. )
I never save plastic bags other than plastic shopping bags which we use for scooping out the cat litter. I use mostly reusable shopping bags, so we get just enough bags for kitty litter. 99% of our food storage plastic is Tupperware... The real stuff stuff, so I have no need for plastics from the grocery store.