We've really never stopped doing this, especially Mrs Duke who grew up on a farm. The list of things I'm not allowed to throw away is long. She saves screw top jars for a friend who makes salsa, wine bottles for her sister who makes wine, Cool Whip (and similar containers) for leftovers, Christmas cookie tins for sewing supplies, etc.
We have a small canister (of a set) full of nothing but sugar/artificial sweetener packets she's liberated from restaurants, as well as packets of catsup/mustard/honey, etc. in the refrigerator. And God forbid I should throw away the odd screw or nail. "Someone can use that," is one of her favorite expressions.
The funny part is she'll take such treasures to my daughter, who in turn graciously accepts them, then throws them away after she leaves.
I save a few things, the oddest being dryer lint. I keep plastic jars of it in our winter survival kits in our cars. It makes a great fire starter, especially with a few drops of hand sanitizer gel.