We all face this same problem, believe me! The desire to save every scrap of potentially useable wood has to be kept under control, or it can really get out of hand. When I moved my whole operation 3 1/2 years ago, I had been in the building in Burbank for 21 years. I had saved and accumulated an enormous amount of scrap wood over those years, and had stashed and squeezed it into every corner of that place. As I was trying to finish up the move of all my machines and stuff (an exhausting adventure), it became obvious how big a problem I had. I was driving myself crazy attempting to pick through the piles and load it up to be moved. I finally reached a point where I hired a couple of guys with a big truck. While I was waiting for them to come over, I took two hours and picked the very best stuff to save, which I loaded myself into boxes in my truck. Then they loaded up all the rest and took it to the dump. Had to be done. I realized how much it would have cost me to move and then store all that scrap wood at my new place.
Until I had cleared out the machines and shelving, it wasn't obvious how much volume and weight of lumber scraps I had managed to save in there, gradually packing it away into every corner. It was several tons that went to the dump.
With that memory, I've been strict with myself at my new place. I'm not going to let myself get to that point again.
A couple of things that help a lot:
I have designated areas where scrap wood goes. Some shelving, vertical racks, organized boxes. All scrap wood must be kept in those areas. When they fill up, I have to sort through and get rid of some. No more piling up scraps in every available corner.
The scraps need to be separated and somewhat organized. If they are in random, dirty piles, I'm not going to take the time to dig through them to find what I need.
Saw scraps into rectangles. Wood scraps that are odd shaped, particularly with points, are really cumbersome to store. They end up going into a rough pile, which wastes space and is hard to sort through. So they don't get used. As soon as I'm done sawing out a body blank or whatever, I immediately take an extra moment to saw the points off the scraps, making them into approximate rectangles. Then they store neatly in shelves and boxes, where they can be easily found and used.
The best storage is steel shelving, with the scrap boards standing up on edge. Or at least keep the shelves close together, so the stacks aren't too deep. If it's too hard to pull out individual pieces, then it might as well be waste wood.
Small pieces of exotics, like cutoffs from fingerboard blanks, are separated into bin boxes on shelves. Those scraps are very useful. I also save long thin strips of exotic fingerboard woods.
Lately, I've found two other useful outlets for scraps: Isaac, whose shop is down the hall, makes artistic wood sculptures. He uses strips of nice hardwoods that we all would throw away. He pays me to rip them to uniform sizes. And Rob Allen (yes, that Rob Allen, whose shop is also down the hall) has a fireplace at his home. So, I keep a box next to my chop saw bench for small hardwood scraps, which he takes home and burns.
It can be heavy, so I chamber it when it's a body core or making up a large piece of a body. I've also used it in necks, but these days stick to maple and walnut...
I always think I'm going to use it, and then hardly ever do. Just little bits here and there. I also figured I have enough other woodworker connections locally that if I really needed a little piece of something, I could probably reach out and find a bit... 
