Depression era parents have a mindset of lack: let's not get rid of anything because we might need it again someday. Another typical mindset is that they bought nice things but never used them, saving them for a "special" occasion that never came. I know my father had a closet full of clothes given as gifts that he never wore; instead he would wear the same worn out but favorite <comfortable> things on a daily basis. Don't get me wrong: he always looked nice, but what was he saving the newer things for? As people age, their lives become simpler. They really don't want or need more gadgets because they like doing things the way they have always done. I didn't understand this when my father used to tell me; I tried to make his life simpler by my standards instead of his. When he died, I found all of my fabulous gifts to him still in boxes -- never opened. It was definitely a wake up call for me.
If you are one of the lucky ones who still have parents living, respect their wishes regarding gifts. When they say they really don't need anything: they mean it. Spending your time with them is their most precious gift. If you can help them with their clutter, do so now before they are gone. Call me if my objective, non-judgmental help would make it easier for you. Sometimes they can be convinced that they don't actually need the physical object: you can reminisce about it, take a picture and give the actual item away. Create a photo album for things they loved. Encourage them to use the things they have saved for "later." Surround them with the things they love right now. And most importantly … give them the gift of your time … creating cherished memories for both of you.