I use various bits from my supply frequently.
I had a can full of nuts/bolts/screws/washers. I had also collected a lot of small glass jars (sold with pimentos I think). One winder I spread my stuff out on a table and sorted into piles of screws, bolts, nuts, etc. Then I sorted each pile into multiple piles roughly by approximate size. I painted the jar lids all silver then labeled them such as "nuts 1", "nuts 2", etc. and put each pile of different size hardware into its own jar. When I need something I can pull out a jar and look through it to see if it is close to what I need. If not then I go to the next jar. When I find a jar of interest I dump it out in a bowl and dig through it to find what I need. Well 10 years later I had a lot more hardware saved up. I didn't want to go through the entire sorting again but I did sort all of it by category- nuts, bolts, screws, etc. Then I put each pile into a thick ziplock back and put in a drawer. I can dump out a quart bag into a bowl and dig through it fairly easily, not as easily as the segregated hardware in a glass jar. Last Christmas I noticed that my wife was throwing out some metal tins that cookies came in so I grabbed them. One now holds my bolts and one holds my screws. It is easy to pull off the big lid and dig through the contents without having to dump any of it out.
During my sorting I had some other smaller categories that got their own bag, such as inserts for attaching things to hollow walls, leftover bits from assembling knocked-down furniture, electrical bits, etc.
Saving hardware is what people with packrat personalities do. I had a friend that did his own projects at home but didn't save anything. He figured when he needed new hardware he would go to the store and buy exactly what he needed rather than spend time saving hardware and going through it searching for what he needed. I can see the point of this except that when I'm doing an impromptu project I don't want to have to stop to go to the store.