I keep all my scraps. Sometimes a couple tiny squares is all it takes for a project. Covering buttons, making hair accessories, small pouches, etc. Depending on the remnant I have left I'll trim a lot down into fat quarters, jelly rolls, or quilting squares though just to have some sort of standard sizing to it. Miniscule scraps I put in a HUGE hurricane vase that I have. It looks cute, and I like pawing through it occasionally to find that perfect little piece for whatever project I may be working on.
I have 3 12x12x12 cubbies full of yardage fabric at the moment, and an underbed tote filled with home decor and outdoor fabrics, plus another tote filled with fleece waiting to be turned into a zillion pairs of lounge pants for Christmas gifts. I'm planning a spare bedroom/storage/pantry/craft room overhaul, and the apparal and quilting fabrics will be ending up on comic book board bolts and on shelving. I also got a free vintage serger (amazing!) that is currently sitting in my garage, so I've got to get that in the house and get that and the sewing machine cranking through my mile long list of projects.
I've also got a yarn problem lol