Papertowel cardboard centers go to DD to play with. She gets 1 about every 4-6 weeks as papertowels are used for cat/dog messes mostly or draining bacon. She decorates them and then uses them to look at things or to yell through!
Cute jars (Aldi has exceptionally cute jars -- especially the square ones for artichoke hearts and the fruit spread roundish ones) are used for repackaging spices or homemade spice mixes. If you can get the label off and paint the lid, they make for a great gift-giving jar. We found that generally the lids just need to be sanded lightly, then primed, then painted. We use spray primer and spray paint; a little goes a long way. We will also use them as change jars or to hold other small objects.
I have a bag full of wax cereal bags; in fact, I have so many right now and have not needed them much that I've stopped collecting them for a moment.
We have these GINORMOUS garbage bags we use on the deep cat box and even though we can't find a smaller bag to work we don't even need the top half of the bag. So now we cut it off and save it so DD can do art projects on top of the bag. When we can no longer use it for that, just gather and throw away.
My plastic bags from the grocery store are saved and given to a food pantry. I prefer to use my reusable bags, but they always wrap meat in the plastic ones in case of messes and I appreciate that. There is rarely a mess so I just save the bags until I have enough to drop off at the food pantry. I heard there may soon be a plastic bag tax; if that happens I'll stop using them altogether and just put my meats in a lined reusable bag that can be cleaned.