For years we saved boxes that things came in. But one time we walked into the garage and we could barely get around. It took most of a day, but we broken them all down and off the the recycler they went. I save a few boxes in case they are needed for sending things.
As for bags, we re-use some and the others go to be recycled, unless they are dirty. When my mother passed away I was in charge of going through and throwing out things that could not be sold or recycled. There were so many bags with more bags in them. I could understand it because when the plastic bags first became popular we all re-used them until they got a tear. But with time we had more than we could use and they tore much more easily. But my family mantra was always, "Never throw anything away." So I came home and got rid of the majority of our plastic bags. Luckily we can take them to Walmart and have them recycled. My parents even brought home paper napkins from restaurants. Which I do that too - but I found a couple boxes filled.