If I have a need of a box in the relatively near future I will save one of an appropriate size. Otherwise they go in recycle. I do save plastic grocery bags as they are used as liners for small waste baskets in the house as well as 'poopy bags' when we walk the dog.
Don't generally save plastic takeout food containers as I have enough reusable containers of the size I like. Will save several paper grocery bags for some garbage needs but not many. Our recycle program is quite handy. We have several 40 gallon plastic bins. Paper; plastic; glass - all in the same bins; no sorting necessary. Pick up is every 2 weeks.